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23h	comment	Equivariant $K$-theory, singular vectors, and flag manifolds I meant the stuff about hyper-geometric functions. Sorry, I should have been more specific.
1d	comment	Equivariant $K$-theory, singular vectors, and flag manifolds OK. I just wonder whether the second paragraph can be pushed to generalized flag manifolds $G/P$ for $P$ parabolic. Do you know any references here? At least for the Borel case.
1d	comment	Equivariant $K$-theory, singular vectors, and flag manifolds You confused notation in the first paragraph. The bundle should be over $M$ and $H$ should be $B$. Is there any reason why don't you suppose that $G/B$ is a flag variety right from the beginning?
May 15	comment	Continuation of homomorphisms of representations… No need to restrict to complex representations. One just has to assume that the characteristic of the field does not divide the order of $G$.
Apr 29	comment	Criterion for nilradical of a maximal parabolic subalgebra to be abelian? bearspace.baylor.edu/Markus_Hunziker/www/… Lemma 2.2
Apr 10	comment	Name for algebra and its tensor products In that case you can just renumber indices $i \to i-1$ and write $U_i$, $i\in \mathbb{Z}_n$. Adding some context would be helpful. Are the variables $U_i$ (anti)commutative?
Apr 4	comment	Density of smooth functions in Sobolev spaces on manifolds I am only vaguely familiar with definition of Sobolev spaces on manifolds via patching local definitions. Thus it seems to me, that if you can prove the density locally, you have it also globally.
Apr 3	comment	Invariance of dynamical system under a transformation @Robert Bryant: I think that users are allowed to edit their posts only if they have high enough reputation. But maybe it applies only to questions and answers can be edited always.
Apr 3	comment	Using Fourier Transform to speed up calculation of forces following an inverse square law This could be also a good starting point: en.wikipedia.org/wiki/…
Apr 3	comment	Using Fourier Transform to speed up calculation of forces following an inverse square law First hit on google: cs.montana.edu/courses/spring2005/580/papers/…
Apr 3	revised	Inversion of complex matrix rewrite the equation
Mar 30	comment	When does a modular form satisfy a differential equation with rational coefficients? Perhaps this could be helpful. mmrc.iss.ac.cn/pub/mm25.pdf/7.pdf
Mar 30	comment	Area of a lattice polygon in terms of its width What is the question here?
Mar 29	asked	easter problem - egg shapes
Mar 22	answered	Inversion of complex matrix
Mar 22	comment	simple roots of a reflection subgroup I've emailed Hunziker about a week ago with no reply so far. I guess I should've cc'ed Enright as well.
Mar 22	revised	simple roots of a reflection subgroup edited tags
Mar 22	asked	simple roots of a reflection subgroup
Mar 14	comment	Hilbert Matrix and Approximation Theory I believe that the answer to your question lies in the paper by Hilbert which you can find on the wikipedia page on Hilber matrix.
Mar 14	comment	smooth connection on exterior power Yes, it does. This question would be more appropriate for math.stackexchange.com
Mar 7	comment	Invariant subbundles of tangent bundle of flag variety Sorry for the jargon. I've edited my "answer" accordingly.
Mar 7	revised	Invariant subbundles of tangent bundle of flag variety fixed reference
Mar 6	answered	Invariant subbundles of tangent bundle of flag variety
Feb 28	comment	translation functors in parabolic category $\mathcal{O}$ Done. The link to (hopefully) improved question is above. Thank you for your time, I greatly appreciate it. Also, let me use this opportunity to thank you for your wonderful book on category $\mathcal{O}$. It is a truly great source of information!
Feb 28	revised	translation functors in parabolic category $\mathcal{O}$ deleted 2940 characters in body; edited title
Feb 28	asked	BGG-like resolutions and translations
Feb 28	comment	translation functors in parabolic category $\mathcal{O}$ I think a better approach is to revert my question to the original version and create a new one.
Feb 28	revised	translation functors in parabolic category $\mathcal{O}$ added 3054 characters in body; edited tags; edited title
Feb 28	revised	translation functors in parabolic category $\mathcal{O}$ edited tags
Feb 27	comment	Exceptional Schur-Weyl Duality Already fixed. Thanks.
Feb 27	revised	Exceptional Schur-Weyl Duality wrong url in second link
Feb 27	answered	Exceptional Schur-Weyl Duality
Feb 13	comment	translation functors in parabolic category $\mathcal{O}$ Thank you for your comments. What if I view $\mathcal{O}^\mathfrak{p}_\lambda$ as a subcategory of $\mathcal{O}_\lambda$ and consider the restriction of the translation functor? My intended application is a cohomology formula for $L_\mathfrak{p}(\lambda+\mu)$ for $\mathfrak{g}$-integral $\lambda$ which is not $\mathfrak{g}$ -dominant.
Feb 13	asked	translation functors in parabolic category $\mathcal{O}$
Feb 11	comment	From Topological to Smooth and Holomorphic Vector Bundles Thanks a lot for your answer and for the ensuing discussion. These issues are usually swept under the rug in introductory courses and can get quite confusing later on.
Jan 27	comment	Why are the holomorphic line bundle sections finite dimensional? I think that the answer to your question lies in the theory of elliptic PDEs. All harmonic functions on a compact Riemannian manifold are constant and a proof of this fact is a matter of calculation. Nevertheless, this fact can be also (at least heuristically) gleaned from the mean value property of harmonic functions. If you want more details I suggest book by Raymond Wells - Differential Analysis on Complex Manifolds.
Jan 18	comment	Infinite dimensional unitary representations of SU(2) for non-half-integer j? @John Baez: Thanks for pointing this out! But I don't see that this is in fact an irreducible representation.
Jan 16	comment	parabolic subalgebras and Cartan decomposition Andrea, would you care to write these comments into an answer so I can award you the bounty?
Jan 16	comment	parabolic subalgebras and Cartan decomposition Agreed, but since he did not posted an answer I cannot give him the bounty. And thank you for your remarks.
Jan 10	comment	Non-trivial representation of second-smallest dimension Well, minimal was not the right word. What I meant to say that the representation with minimal dimension among all representations is the same as the representation which has the smallest dimension amongst fundamental representations.
Jan 10	comment	Non-trivial representation of second-smallest dimension It follows from the Weyl dimension formula that the fundamental representations have minimal dimensions. So you only have to check the dimensions of these.
Jan 8	comment	parabolic subalgebras and Cartan decomposition @Andrea Altomani: I don't know. Hence the bounty. :) By the way - how do you show that such a $\mathfrak{q}$ is a parabolic subalgebra?
Jan 3	comment	parabolic subalgebras and Cartan decomposition No, in my context $\theta$ is linear. The real parabolic subalgebras can come from different real versions of $G$.
Jan 3	comment	parabolic subalgebras and Cartan decomposition There is an abuse of notation. Cartan involution $\theta$ can mean an involution either on a real Lie group or on a real Lie algebra. Moreover you can always complexify the algebra and denote the extended involution by the same letter and still call it Cartan involution. You can extended it to a complex linear involution of the complexification or to a complex antilinear (i.e. $\theta (i X) = -i\theta(X)$) involution of the complexification. I've seen both and the authors still called their extension Cartan involution and denoted it by the same letter. Some authors use $\Theta$ at group level.
Jan 3	asked	parabolic subalgebras and Cartan decomposition

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