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

location  India  
age  
visits  member for  2 years, 7 months 
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interested in representations of groups, algebraic groups, arithmetic groups, rigidity, and related automorphic forms. Recently interested in braid groups and configuration spaces.
8h

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Action of the pure braid group on the commutator subgroup of a free group
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18h

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Action of the pure braid group on the commutator subgroup of a free group
in short, you are asking if the kernel of the Gassner representation is nontrivial; I think this isan open problem (though it is known that the Burau rep is not faithful, and Burau and Gassner are related, to the best of my knowledge, it is not known whether Gassner is faithful. You may ask Misha Kapovitch about this 
18h

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Action of the pure braid group on the commutator subgroup of a free group
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19h

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Action of the pure braid group on the commutator subgroup of a free group
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19h

answered  Action of the pure braid group on the commutator subgroup of a free group 
1d

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What is the cubic casimir element of sl_3?
you may want to look at the book by Humphreys on Lie algebras. The explicit isomorphism between the associated graded of the enveloping algebra of a semisimple Lie algebra $\mathfrak g$ and the symmetric algebra of $\mathfrak g$ is given there from which you can deduce that the space of invariants of the enveloping algebra (i.e. its centre) is isomorphic to the space of $\mathfrak g$ invariants in the symmetric algebra; the latter is a polynimial algebra with some well chosen generators. In your case, there is one in degree three, namely the determinant of a traceless $3\times 3$ matrix. 
Nov 21 
reviewed  Approve suggested edit on When does the zeta function take on integer values? 
Nov 21 
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Discrete subgroup of complex orthogonal group
If $n\geq 5$, then all lattices are "arithmetic" and classification arises from Galois cohomology , Hasse principle, etc.You have to see the books of Margulis and of PlatonovRapinchuk for details. If $n\leq 4$, then there are many more lattices. 
Nov 21 
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Discrete subgroup of complex orthogonal group
Do you want discrete subgroups with finite covolume or only discrete subgroups? In any case, there are many examples; if you want only discrete subgroups, a Schottky construction (pingpong) gives you plenty. If you ask for lattices, many discrete groups can be constructed as unit groups of quadratic forms over an imaginary quadratic extension; a full classification is possible, if $n\geq 5$. 
Nov 20 
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A good book on adeles and ideles
Weil also has a book "Adeles and Algebraic Groups" where he interprets a theorem of Siegel in terms of "Tamagawa measures" which has a fairly detailed discussion of adeles 
Nov 20 
answered  Reductive subgroup and its derived subgroup with an irreducible represenation 
Nov 19 
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What is the nilradical of $\mathfrak{gl}_n$?
it is zero. This is really a consequence of definitions, and these questions are better suited to math stackexchange 
Nov 19 
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Analytic function avoiding elements of the modular group
thank you; I missed this. 
Nov 19 
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Who first noticed that the Hilbert symbol is a Steinberg symbol ?
@Humphreys: See also Proposition(3.1) of BassMilnorSeree where they prove that the norm residue symbol is a Mennicke Symbol. 
Nov 19 
reviewed  Approve suggested edit on Classification of the Kähler Structures on the Sphere 
Nov 15 
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How can the existence of this expression with Cartan matrix be shown using Killing form?
Does it mean this is a homework which we are supposed to do? 
Nov 14 
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Who first noticed that the Hilbert symbol is a Steinberg symbol ?
@Humphreys: It is possible that BassMilnorSerre consider only the global Hilbert symbol and Mennicke symbol, but not the local Hilbert symbol and (Steinberg) symbol 
Nov 14 
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Who first noticed that the Hilbert symbol is a Steinberg symbol ?
@Humphreys: They use it all the time: that Mennicke symbol is the Hilbert symbol is used in computing the congruence subgroup kernel (e.g see Theorem (3.6) of BassMilnor Serre paper). The symbol $ (,)$ in Theorem (3.6) is the Hilbert symbol. 
Nov 14 
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Who first noticed that the Hilbert symbol is a Steinberg symbol ?
For the group SL_n this was called the Mennicke symbol in BassMilnorSerre paper and they identify it with hilbert symbol, therefore, maybe Mennicke noticed it . 
Nov 13 
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Applications of the Small and Great Theorems of Picard
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