Alain Valette
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Registered User
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Apr 29 |
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Borel’s Paris Lectures @Jim: "Hard to locate" is quite correct, for the book version: I was lucky to find my own copy at a "bouquiniste", along the Seine in Paris, a couple of years ago! |
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Apr 27 |
awarded | ● Nice Question |
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Apr 24 |
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Ordered groups - examples Oops, thank you Yves, indeed my remark on $Homeo^+(\mathbb{R})$ is false. One day it will be possible to edit comments on MO. |
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Apr 21 |
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Are $K$-finite vectors dense in irreducible Banach representations? With due respect to Lang's memory, whom I deeply admire: in 1981-82, when I was a 2nd year graduate student, my supervisor at Paris gave me this book $SL(2,\mathbb{R})$ and commented: "If you want to learn representation theory, find all the mistakes in Lang's book!" That was an extremely good advice. |
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Apr 21 |
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Ordered groups - examples Follow-up to Qiaochu's comment: two answers posted on math.stackexchange.com/questions/365660/… I found the one by Tournesol interesting. Recall that a group of orientation-preserving homeo's of $\mathbb{R}$ admits a total, bi-invariant ordering (with $f\leq g$ iff $f(x)\leq g(x)$ for every $x$). Since $B(m,1)$ embeds in the affine group of $\mathbb{R}$, it admits such an ordering. |
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Apr 21 |
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Possible directions in noncommutative geometry Please read: mathoverflow.net/howtoask To be more positive: don't you have in your department a professor / post-doc / more advanced PhD student with whom you could discuss this (rather vague) question over coffee? |
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Apr 21 |
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special primes with p'=4p+1 This brings to mind Sophie Germain primes, i.e. primes $p$ for which $2p+1$ is a prime, and whether there are infinitely many such primes is a notorious open question: en.wikipedia.org/wiki/Sophie_Germain_prime |
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Apr 21 |
answered | Does every irreducible Banach representation admit a $K$-finite vector? |
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Apr 20 |
answered | Gelfand representation and functional calculus applications beyond Functional Analysis |
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Apr 18 |
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Which p-adic algebraic groups are type I? @Marc: Yes there is something weird with the link, that I couldn't fix. I put the reference instead. |
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Apr 18 |
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Which p-adic algebraic groups are type I? Replaced a broken link; added 84 characters in body |
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Apr 18 |
awarded | ● Yearling |
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Apr 16 |
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Are the groups $C( \mathbb{R} ; U(n) )$ isomorphic? I think that the $C(X,U(n))$'s can be distinguished by observing that the minimal degree of a unitary irreducible representation of $C(X,U(n))$, not of degree 1, must be $n$. |
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Apr 14 |
asked | Which p-adic algebraic groups are type I? |
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Apr 11 |
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Harmonic analysis on the Heisenberg group Can you motivate the question a bit? |
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Mar 31 |
awarded | ● Necromancer |
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Mar 29 |
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Applications of n-dimensional crystallographic groups This is more of an application of Bieberbach's theorems: in the proof of quasi-isometric rigidity of $\mathbb{Z}^n$ given in that paper: arxiv.org/abs/math/0509527 it is proved that a group $G$ quasi-isometric to $\mathbb{Z}^n$ admits a proper isometric action on some (finite-dimensional) Euclidean space. By Bieberbach, the group $G$ is virtually abelian, so contains a $\mathbb{Z}^m$ of finite index. Finally $m=n$ by invariance of growth under quasi-isometry. |
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Mar 29 |
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Unbounded representations of groups @ Kate: I think that Taka's excellent comment comes very close to an answer... |
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Mar 29 |
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Unbounded representations of groups @ Yves, Mikael: I feel psycho-analyzed, but you are right about how I interpreted Kate's question... (no unbounded operators in my interpretation). |
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Mar 28 |
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Unbounded representations of groups My understanding of Kate's question is this: does any f.g. group admit a proper, affine action on a Hilbert space? Am I correct? |
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Mar 28 |
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Unbounded representations of groups And my guess is that, here, a representation is just a homomorphism $G\rightarrow GL({\cal H})$. |
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Mar 28 |
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Unbounded representations of groups I think that Kate meant UNbounded... |
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Mar 23 |
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The Periodic Schrödinger Group This is an instance of Stone's theorem en.wikipedia.org/wiki/Stone's_theorem_on_one-parameter_unitary_groups |
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Mar 20 |
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Is there a database somewhere for sharing translations of mathematical works? (Or, is anyone interested in a translation of a letter Weil wrote to de Rham in 1946?) Corrected spelling of de Rham; edited title |
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Mar 20 |
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Spectral synthesis for central functions on locally compact groups Have you looked at Chapters 17 and 18 of Dixmier's $C^*$-book? I feel they are somewhat related to your question... |
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Mar 20 |
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Spectral synthesis for central functions on locally compact groups deleted 3 characters in body |
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Mar 20 |
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Spectral synthesis for central functions on locally compact groups Corrected formula (1) and added one tag |
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Mar 17 |
awarded | ● Nice Answer |
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Mar 17 |
accepted | An expander (?) graph |
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Mar 16 |
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Nilpotent subgroups of uniform finite index You should make explicit that $N$ is normalized by $K$. |
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Mar 16 |
answered | An expander (?) graph |
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Mar 14 |
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The Work of Pierre Deligne I wonder how Deligne will feel if he reads that question... |
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Mar 11 |
awarded | ● Nice Answer |
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Mar 11 |
answered | how do I withdraw my submitted paper? |
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Mar 9 |
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If e^itπ is algebraic , is $t$ a rational number. @quid: I admit, I read the question too fast... |
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Mar 9 |
answered | Is there an editors checklist for mathematics? |
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Mar 9 |
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If e^itπ is algebraic , is $t$ a rational number. en.wikipedia.org/wiki/Gelfond–Schneider_theorem |
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Mar 8 |
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Idempotents in compact semigroups en.wikipedia.org/wiki/Ellis–Numakura_lemma |
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Mar 6 |
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What are the sub $C^*$-algebras of $C(X,M_n)$? I don't think there is a simple description: you can have $C^*$-subalgebras with non-Hausdorff spectra (simplest example: continuous functions $[0,1]\rightarrow M_n$ which are diagonal at $0$); and if you assume your $C^*$-subalgebra to be homogeneous (i.e. all its irreducible rep's are of the same dimension), then you have the $K$-theory of $C(X)$ showing up (if $p$ is a self-adjoint idempotent in $M_n(C(X))$, look at the subalgebra $pM_n(C(X))p$). |
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Mar 4 |
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Taking direct sums in $K$-theory in Kirchberg-Phillips classification @Ulrich: OK, then I eventually made sense of the OP. But can you describe, for instance, the operation on Kirchberg algebras that flips $K_0$ and $K_1$, i.e. which has the same effect on K-theory as tensoring by $C_0(\mathbb{R})$? |
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Mar 4 |
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Taking direct sums in $K$-theory in Kirchberg-Phillips classification removed a tag |
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Mar 4 |
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Taking direct sums in $K$-theory in Kirchberg-Phillips classification You want to know which operation on Kirchberg algebras corresponds to direct sum of $K$-groups (of course direct sum of simple algebras takes you out of simple algebras). But for your question to make sense, you need to specify the range of the $K$-theory invariants (i.e. which are the pairs of abelian groups that you can get as $(K_0,K_1)$ of a Kirchberg algebra). If direct sum of $K$-groups takes you out of the range, your question may be meaningless... |
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Mar 2 |
accepted | On the descent homomorphsim of Kasparov equivariant KK theory |
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Mar 2 |
answered | On the descent homomorphsim of Kasparov equivariant KK theory |
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Mar 2 |
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The irreducible character of $2.L_2(p)$ where p is a prime @Stefan: you mean that $2.L_2(P)$ is $SL_2(p)$? Oh boy... |
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Mar 2 |
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discrete subgroups of Lie groups and actions on homogeneous spaces I understood the OP as Lee (nice answer, BTW!), and Yves'comment made me realize that the question is ambiguous... |
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Mar 2 |
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The irreducible character of $2.L_2(p)$ where p is a prime Thanks, Jay, for explaining that $L_2(p)$ is just $PSL_2(p)$. But what is $2.L_2(p)$ exactly? |
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Feb 18 |
awarded | ● Necromancer |
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Feb 18 |
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Diff(M) and connectedness $Diff(M)$ is the group of diffeomorphisms, and the question is how properties of $Diff(M)$ reflect in topological properties of $M$. |
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Feb 18 |
awarded | ● Disciplined |
