4,174 reputation
11224
bio website math.tifr.res.in/~venky
location India
age
visits member for 2 years, 7 months
seen 1 hour ago

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


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
edited body
Nov
13
revised Applications of the Small and Great Theorems of Picard
"has nontrivial" replaced by "has no non-trivial"
Nov
9
reviewed Approve suggested edit on Which are the recommended books for an introductory study of complex manifolds?
Nov
8
comment Restriction of scalars for the adjoint representation of $SL_2(\mathbb F_q)$
@Michor: thank you. After reading the ans carefully, I see that you were looing at the 3 dimensional adjoint module.
Nov
8
revised Restriction of scalars for the adjoint representation of $SL_2(\mathbb F_q)$
deleted 522 characters in body
Nov
8
comment Restriction of scalars for the adjoint representation of $SL_2(\mathbb F_q)$
Are you looking at the two dimensional rep of $V$? Joel looks at the three dimensional adjoint representation $V$.
Nov
7
revised Restriction of scalars for the adjoint representation of $SL_2(\mathbb F_q)$
added 1662 characters in body