Abdelmalek Abdesselam
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Registered User
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May 14 |
answered | What is the “fundamental theorem of invariant theory” ? |
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May 13 |
awarded | ● Nice Answer |
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May 8 |
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A basis of the symmetric power consisting of powers @Jesko: see my last edit. |
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May 8 |
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A basis of the symmetric power consisting of powers added 1831 characters in body |
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May 1 |
revised |
A basis of the symmetric power consisting of powers added 494 characters in body |
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May 1 |
answered | A basis of the symmetric power consisting of powers |
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May 1 |
answered | Generate a higher degree symmetric polynomial from an existing one |
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Apr 25 |
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Does Physics need non-analytic smooth functions? Not sure this a good example. For some field theories constructed rigorously the function is still analytic even though the Taylor series has zero radius of convergence. The issue is the location of the point around which the Taylor expansion is made: in the middle of the domain of analyticity (ordinary summation which requires positive radius of convergence) versus on the boundary (Borel summation). |
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Apr 25 |
answered | An expression with an alternating trilinear form, written in terms of the determinant and a symmetric bilinear form |
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Apr 17 |
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Is rigour just a ritual that most mathematicians wish to get rid of if they could? Of course. But I think the issue here rather is about published mathematical papers telling insights and intuitions yet without the gory details. |
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Apr 15 |
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How would I apply Wick’s theorem to the time-ordered product of three fields? it's done on page 181 of Itzykson-Zuber 1980 edition. |
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Apr 3 |
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Trivial p-adic measures @Steve: You need to give more details, otherwise it is not very respectful of people who would make the effort of answering your question. Is mu a real valued positive measure? if so, is the sigma algebra that of Borel sets etc. |
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Mar 28 |
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How to show a certain determinant is non-zero This is very pretty. |
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Mar 27 |
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Partial linearization near a hyperbolic fixed point--Classical scattering added 133 characters in body |
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Mar 22 |
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Partial linearization near a hyperbolic fixed point--Classical scattering added 16 characters in body |
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Mar 22 |
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Partial linearization near a hyperbolic fixed point--Classical scattering edited tags |
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Mar 21 |
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Partial linearization near a hyperbolic fixed point--Classical scattering added 1692 characters in body; edited title |
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Mar 20 |
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Partial linearization near a hyperbolic fixed point--Classical scattering @Adam: Thanks I will look at Sec 6. |
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Mar 20 |
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Partial linearization near a hyperbolic fixed point--Classical scattering @Adam: I was looking at this paper yesterday but it is quite long and I have yet to see where the kind of theorem I am interested in is embedded. |
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Mar 20 |
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Partial linearization near a hyperbolic fixed point--Classical scattering edited tags |
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Mar 20 |
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Partial linearization near a hyperbolic fixed point--Classical scattering @Peter: I would not say "strikingly". My question is quite unsurprisingly related to this kind of questions simply because it explores extensions of normal form theory in the direction of weaker statements than e.g. full linearizations. |
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Mar 19 |
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Partial linearization near a hyperbolic fixed point--Classical scattering added 6 characters in body |
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Mar 19 |
asked | Partial linearization near a hyperbolic fixed point--Classical scattering |
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Mar 18 |
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Invariants of a set of real unit vectors in 3d space, under SO(3) @Piotr: degree bounds are not easy either. For binary form CIT there is an old one by Jordan see: www.math.lsa.umich.edu/~hderksen/preprints/bound.ps I don't know if it has been improved recently. |
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Mar 4 |
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Extremely messy proofs @anon: indeed, there is a lot more in that article than what we now know as the Hilbert Basis Thm: the Hilbert polynomial, the Hilbert Syzygy Thm, the application to rings of invariants via averaging over SU(n) done by way of Cayley's omega operator... |
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Mar 4 |
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What is a Gaussian measure? you can define being Gaussian by saying the moments are given by the Isserlis-Wick's theorem or the log-moment generating function is quadratic. |
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Mar 4 |
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Higher dimensional Bezout via Hilbert polynomials: a reference. @aglearner: there are many places depending on the level of sophistication you want. There is the book by Gelfand, Kapranov and Zelevinsky. The book "Using Algebraic Geometry" by Cox Little and O'Shea. A quick intro is in the first edition of Modern Algebra by van der Waerden. |
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Mar 4 |
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Modern developments in finite-dimensional linear algebra @Felipe and Timur: it seems we were thinking of different papers. Felipe's are about upper bounds on complexity while the ones I mentioned in my answer are about lower bounds. Sorry for being such a pessimist. |
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Mar 4 |
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Higher dimensional Bezout via Hilbert polynomials: a reference. @aglearner: How about using multidimensional resultants? If you consider Res(F_1,...,F_n,U) where U is the linear form defining a variable hyperplane, Bezout is just the statement that the above expression is a completely factorized polynomial in U of degree d_1...d_n. |
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Mar 1 |
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Access to a preprint by D. N. Verma very nice answer |
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Feb 28 |
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what’s the motivation of Weyl calculus ? was it cut-off because of the number of characters? that's hilarious. |
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Feb 28 |
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real symmetric matrix has real eigenvalues - elementary proof added 66 characters in body |
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Feb 28 |
answered | Modern developments in finite-dimensional linear algebra |
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Feb 27 |
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Exceptional Schur-Weyl Duality your second link goes to a paper of Deligne and Gross instead of that by Bruno Blind. |
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Feb 27 |
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Modern developments in finite-dimensional linear algebra @Gerry: major enough to get published in JAMS. |
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Feb 27 |
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real symmetric matrix has real eigenvalues - elementary proof added 5 characters in body |
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Feb 27 |
answered | real symmetric matrix has real eigenvalues - elementary proof |
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Feb 27 |
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Homogenous polynomials as sum or differences of squares and symmetric polynomials At the risk of stating the obvious I think Per is well able to correct these trivialities about degrees. |
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Feb 27 |
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Should one attack hard problems? I think Frank is right. Not a good idea and not very fair to close this question. |
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Feb 26 |
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What mathematical treatment is there on the renormalization group flow in a space of Lagrangians? added 271 characters in body |
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Feb 26 |
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Homogenous polynomials as sum or differences of squares and symmetric polynomials @Per: you mean the degree of Q is 1/2 that of P...So you are looking at a higher degree version of Gauss's decomposition of quadratic forms? |
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Feb 21 |
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What is quantum Brownian motion? I think the review by Erdos has nothing to do with non-commutative probability. The goal is to show that in some limit the quantum particle in a disordered medium behaves according to classical Brownian motion, with emphasis on the word "classical". |
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Feb 20 |
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Derivation of Grassmann valued functional maybe better the physics version of stack exchange. Your first formula with just \theta^{\ast}(x) is wrong. The second with also the exponential is correct. |
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Feb 19 |
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Generalized elementary symmetric functions Schlafli with one "l" apparently. |
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Feb 19 |
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A nice generating set for the symmetric power of an algebra it's even older than that, it is in the 1852 paper by Schlafli on resultants. |
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Feb 19 |
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A nice generating set for the symmetric power of an algebra see my comment to MO 122287. |
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Feb 19 |
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Generalized elementary symmetric functions I think these are just multisymmetric polynomials. See the page by Emmanuel Briand that I link to in my answer to MO109340. He has a paper on when the algebra of such polynomials is generated by elementary multisymmetric polynomials. The question MO122207, I think, can be answered using multisymmetric power sums. These are old results by Schlaffli and Junker. |
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Feb 15 |
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Invariant polynomials for a product of algebraic groups added 576 characters in body |
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Feb 14 |
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Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases? I just saw an interesting unpublished paper by Agaoka on these plethysms. It can be found on Google Scholar by searching his name and "decomposition formulas of the plethysm". |
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Feb 14 |
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Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases? the paper by Thrall is in American J. Math vol. 64 p. 371. but I just now saw that you referred to it in your recent work. |
