bio | website | math.tifr.res.in/~venky |
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location | India | |
age | ||
visits | member for | 2 years, 7 months |
seen | 1 hour ago | |
stats | profile views | 2,497 |
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 |
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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 Platonov-Rapinchuk 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 (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 |
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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 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 |
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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 Bass-Milnor-Serre 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 Bass-Milnor 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 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 |
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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 |
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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 |