4,184 reputation
11224
bio website math.tifr.res.in/~venky
location India
age
visits member for 2 years, 7 months
seen 4 hours ago

interested in representations of groups, algebraic groups, arithmetic groups, rigidity, and related automorphic forms. Recently interested in braid groups and configuration spaces.


8h
revised Action of the pure braid group on the commutator subgroup of a free group
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18h
comment 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 non-trivial; 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
revised Action of the pure braid group on the commutator subgroup of a free group
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19h
revised Action of the pure braid group on the commutator subgroup of a free group
added 307 characters in body
19h
answered Action of the pure braid group on the commutator subgroup of a free group
1d
comment 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 semi-simple 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
comment 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 Platonov-Rapinchuk for details. If $n\leq 4$, then there are many more lattices.
Nov
21
comment 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 (ping-pong) 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
comment 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
comment 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
comment Analytic function avoiding elements of the modular group
thank you; I missed this.
Nov
19
comment Who first noticed that the Hilbert symbol is a Steinberg symbol ?
@Humphreys: See also Proposition(3.1) of Bass-Milnor-Seree 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
comment 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
comment Who first noticed that the Hilbert symbol is a Steinberg symbol ?
@Humphreys: It is possible that Bass-Milnor-Serre consider only the global Hilbert symbol and Mennicke symbol, but not the local Hilbert symbol and (Steinberg) symbol
Nov
14
comment 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 Bass-Milnor Serre paper). The symbol $ (,)$ in Theorem (3.6) is the Hilbert symbol.
Nov
14
comment Who first noticed that the Hilbert symbol is a Steinberg symbol ?
For the group SL_n this was called the Mennicke symbol in Bass-Milnor-Serre paper and they identify it with hilbert symbol, therefore, maybe Mennicke noticed it .
Nov
13
revised Applications of the Small and Great Theorems of Picard
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