bio | website | math.tifr.res.in/~venky |
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location | India | |
age | ||
visits | member for | 3 years, 2 months |
seen | 55 mins ago | |
stats | profile views | 2,754 |
interested in representations of groups, algebraic groups, arithmetic groups, rigidity, and related automorphic forms. Recently interested in braid groups and configuration spaces.
Jun 26 |
comment |
Does the proof of Picard's theorem become simpler by increasing the number of points that are not attained?
why do you wish to know this? |
Jun 19 |
comment |
Does this extension of Hodge structures split over $\mathbb{Q}$?
this extension may be viewed as modules over the Mumford-Tate group $G$ associated to $H^1$ of the curve. $G$ is reductive since the curve is smooth projective. Hence the extension splits |
Jun 18 |
comment |
minimal polynomial of unipotents in orthogonal group
I think (I made a hasty calculation) all odd $d$ less than $2l$ and all even $d$ less than or equal to $l$ will appear |
Jun 18 |
comment |
minimal polynomial of unipotents in orthogonal group
this can again be read off from SL(2) representation theory. If a rep of SL(2) is to preserve a non-degenerate quadratic form, then the multiplicity of an even (dimensional) irreducible representation must be even. This is the only constraint. Now take the principal SL(2) in a product of these symplectic and orthogonal groups and the unipotent of SL(2) in the product is your general unipotent. The $d$ is the largest dimensional irrep of SL(2) occurring in this even dimensional rep. |
Jun 18 |
answered | minimal polynomial of unipotents in orthogonal group |
Jun 13 |
reviewed | Approve M is an R-module which is not finitely generated. is it true that $\inf \{ i| H^i_I(M)\neq 0 \}\le ht_M I?$ |
May 2 |
awarded | Excavator |
May 2 |
revised |
fundamental groups of curves
added 1 character in body |
Apr 28 |
awarded | Yearling |
Apr 24 |
revised |
Which compact groups have finitely many irreducible representations of each dimension?
added 93 characters in body |
Apr 24 |
answered | Which compact groups have finitely many irreducible representations of each dimension? |
Apr 19 |
comment |
How do we see the rank of the braid group?
if by rank you mean minimal number of generators, then the braid group is two generated and hence has rank two. |
Mar 11 |
comment |
every element with eigenvalue 1
Every connected compact simple Lie group acts on its adjoint representation with the property that $1$ is an eigenvalue for every element. |
Mar 4 |
answered | Residual finiteness: why do we care? |
Mar 3 |
comment |
generalization of highest weight theorem for semisimple lie algebras
Of course, then the representation is not absolutely irreducible, and the highest weight space over the reals, is two dimensional |
Mar 3 |
answered | generalization of highest weight theorem for semisimple lie algebras |
Mar 2 |
comment |
Are Zariski connected and closed semisimple subgroups of semisimple and simply connected algebraic groups again simply connected?
No. $H$ need not be simply connected |
Mar 2 |
comment |
Embedding rational simple algebras in the real quaternions
See the following question; I think it is relevant.mathoverflow.net/questions/120777/… |
Feb 25 |
revised |
Canonical representation of $\operatorname{SL}(2,\mathbb{R})$ on $L^2(\mathbb{R}^2)$
added 36 characters in body |
Feb 24 |
awarded | Nice Answer |