bio  website  math.tifr.res.in/~venky 

location  India  
age  
visits  member for  2 years, 4 months 
seen  7 hours ago  
stats  profile views  2,323 
interested in representations of groups, algebraic groups, arithmetic groups, rigidity, and related automorphic forms. Recently interested in braid groups and configuration spaces.
7h

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Least collaborative mathematician
+1 for "Betti number" 
11h

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Conceptual algebraic proof that Grassmannian is closed in Plucker embedding
I checked; this is standard terminology. 
13h

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Conceptual algebraic proof that Grassmannian is closed in Plucker embedding
Sorry: I may have used a nonstandard terminology. I do mean that the image of a connected $X$ under a dominant map contains a dense open set. 
14h

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A KarrassSolitar theorem for surface groups
Does not a comparison of "Euler characteristics indicate that $N$ must be free, and if $n$ is the number of generators of $N$ , then $1n=q(22g)$ which shows that $q$ the index must be finite? 
19h

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Conceptual algebraic proof that Grassmannian is closed in Plucker embedding
added 48 characters in body 
19h

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Weyl's construction for symplectic groupsan exercise in Fulton and Harris's book
Moreover, the quotient $\wedge ^s V /\Omega ^* \wedge ^{s2}V$ is irreducible, with highest weight $x_1+\cdots+x_s$ in the obvious notation 
20h

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Conceptual algebraic proof that Grassmannian is closed in Plucker embedding
edited body 
20h

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Conceptual algebraic proof that Grassmannian is closed in Plucker embedding
@David: if $Gv$ is an orbit, then the complement of $Gv$ in its closure has smaller dimension by the dominant mapping theorem; of course, in a beginning course on algebraic geometry, I do not know if this is proved before one gets to Grassmannians 
21h

answered  Conceptual algebraic proof that Grassmannian is closed in Plucker embedding 
22h

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Weyl's construction for symplectic groupsan exercise in Fulton and Harris's book
Clearly there is a map from $\wedge ^{s2}V \otimes \wedge ^2 V$ into $\wedge ^s V$. Since $\wedge ^2 V$ contains a vector invariant under the symplectic group (namely the invariant symplectic form in the dual $V^*$, we have a map from $\wedge ^{s2}V$ into $\wedge ^s V$. 
2d

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Go I Know Not Whither and Fetch I Know Not What
fixed grammar 
Sep 15 
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A pSylow of a group $G$ is characteristic in its normalizer $N_G(S)$?
this is a beginner course exercise and not meant for MO. 
Sep 14 
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A function canonically associated to an irreducible representation in L^2(M) for a Riemannian Gmanifold M. Who has seen it?
The map is equivariant for the action of $G$ 
Sep 14 
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A function canonically associated to an irreducible representation in L^2(M) for a Riemannian Gmanifold M. Who has seen it?
The evaluation at $x\in M$ gives a map $\phi$ from $M$ into the dual $V^*$ of $V$; the function $v$ is simply (up to a fixed scalar multiple) the $G$ invariant norm on $V^*$ applied to $\phi (x)$ for $x\in M$; you can define this for any set $X$ on which $G$ acts, in place of $M$. 
Sep 13 
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Are irreducible matrix algebra neccesarily simple?
Part of the Wedderburn theory is that if an algebra has a faithful irreducible representation, then it is semisimple. 
Sep 13 
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quasisplit algebraic group
A ternary quadratic form $F$ over a number field has quasisplit $SO(F)$ if and only if $F$ is equivalent to the form $xy+z^2$. 
Sep 13 
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Are irreducible matrix algebra neccesarily simple?
This is a consequence of Wedderburn theory; the answer is yes. 
Sep 13 
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quasisplit algebraic group
Given a nondegenerate quadratic form $F$ in 2n variables, the group $SO(F)$ is quasisplit if and only if $F$ may be written a direct sum of $n$ hyperbolic forms> If $F$ is a form in $2n+1$ variables, $F$ is a direct sum of $n$ hyperbolic forms plus the form $x^2$. There is a similar description for unitary groups. 
Sep 13 
revised 
Kernel of the character of congruence groups
fixed grammar 
Sep 8 
reviewed  Edit suggested edit on Hilbert Class fields and Pure cubic fields 