All Questions
Tagged with kt.k-theory-and-homology algebraic-groups
9 questions
2
votes
0
answers
162
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Equivariant Künneth formula for partial flag variety
Let $G$ be a simply connected simple algebraic group over $\mathbb{C}$. Let $P$ be a parabolic subgroup of $G$, $\mathscr{F}:=G/P$ the partial flag variety associated to $P$. For a $G$-variety $X$, ...
- 653
4
votes
1
answer
418
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Definition of Chow quotient
I am reading M. M. Kapranov's paper "Chow quotients of Grassmannians. I." (English) in Sergej Gelfand (ed.) et al., I. M. Gelfand seminar. Part 2: Papers of the Gelfand seminar in ...
- 41
38
votes
0
answers
5k
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Homology of $\mathrm{PGL}_2(F)$
Update: As mentioned below, the answer to the original question is a strong No. However, the case of $\pi_4$ remains, and actually I think that this one would follow from Suslin's conjecture on ...
- 21.3k
10
votes
3
answers
725
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Reduction mod $n$ of symplectic group
Let $g,n$ be positive integers, is there a reference that $\mathrm{Sp}(2g,\mathbb{Z})\to\mathrm{Sp}(2g,\mathbb{Z}/n\mathbb{Z})$ is surjection?
The only reference I could find is lemma 5.16 in Deligne–...
user39380
8
votes
1
answer
424
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State of the art knowledge about homology of $SL_2(k[t,t^{-1}])$
What is the current state of knowledge of the group homology of $SL_2(k[t,t^{-1}])$?
I am mostly interested in the case $k$ is algebraically closed of characteristic zero. The most recent work I am ...
- 18.7k
14
votes
2
answers
2k
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Symplectic K-theory
For a ring $R$ consider symplectic K-theory defined as follows: let $\operatorname{Sp}(R) = \lim_n \operatorname{Sp}_{2n}(R)$, let $\operatorname{ESp}(R)$ be the subgroup generated by elementary ...
- 2,050
1
vote
0
answers
251
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The definition of $SK_1$ for an arbitrary ring
Let $R$ be a unitary associative ring. If $R$ is commutative, then one defines $SK_1(R)$ as the quotient $$SK_1(R)=SL(R)/E(R)$$ (Definition 2.8 of http://dmle.cindoc.csic.es/pdf/...
- 1,418
8
votes
1
answer
561
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Homology of special linear group over local field
I am trying to compute the group
$H_1(\mathrm{SL}_2(\mathbb{Z}_2),M)$, where $\mathbb{Z}_2$ are $2$-adic integers and M is a module $\mathbb{Z}_2 \oplus \mathbb{Z}_2$. I suppose that the group acts ...
- 4,316
9
votes
1
answer
820
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Quantum equivariant $K$-theory and DAHA.
Theorem 3.2 of the paper "Quantum cohomology of the Springer resolution" by Braverman, Maulik and Okounkov relates equivariant quantum cohomology of the cotangent bundle of $G/B$ to the trigonometric ...