All Questions
Tagged with equivariant rt.representation-theory
8 questions
0
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43
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Endomorphism algebra of equivariant maps of isotypic module
Let $A$ be a simple Artinian $K$-algebra with a minimal left ideal $M$. Here, $M$ can be viewed as a simple left $A$ module, and, by Schur's lemma, $D=\text{End}_A(M)$ is a $K$-algebra. By Wedderburn-...
- 143
1
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1
answer
95
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Representation of equivariant maps
Let $n,m,k$ be positive integers. Consider the action of symmetric group $S^n$ on $\mathbb{R}^{n\times i}$ (for $i\in \{m,k\}$) by permuting rows; i.e. for each $\pi\in S^n$ and every $n\times i$ ...
- 5,405
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1
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What is equivariant chains on a representation sphere?
For a finite group $G$ and a finite-dimensional real representation $V$ of $G$, denote by $S^V$ the one-point compactification of $V$, with basepoint at infinity.
What is the reduced chain complex $...
- 18.7k
8
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Interactions (functors) between equivariant sheaves for different groups?
Let $G$ be a finite group and $k$ a field (alg. closed char 0 for simplicity).
To every $G$ set $X$ we can assign the category of $G$-equivariant sheaves of $k$-vector spaces $Sh_G(X)$. It is ...
- 7,799
6
votes
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114
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2-functoriality of equivariant derived categories
I am wondering about the 2-functoriality in equivariant derived categories, and I hope that someone can clarify... (apologies if this is a stupid question)
For the more precise formulation, recall ...
- 17.4k
1
vote
1
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690
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Beilinson-Bernstein localization: $\mathfrak{g}$ action on $G$-equivariant sheaf
I have a few elementary questions related to Beilinson-Bernstein localization.
Let $G$ be a semisimple algebraic group over $\mathbb{C}$ with Lie algebra $\mathfrak{g}$. Consider the setup of ...
- 174
6
votes
2
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917
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Do fixed point sets in equivariant crepant resolutions have the same cohomology? How about for the specific case of Nakajima quiver varieties?
A crepant resolution $f:Y\to X$ is a resolution of singularities with $f^*(K_X)=K_Y$. Crepant resolutions do not always exist, and when they exist they may not be unique. However, different crepant ...
- 2,372
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Why is the Nil-Hecke Algebra appearing?
The Nil-Hecke algebra is defined to be the subalgebra of the endomorphism ring of $\mathbb{C}[x_1,\ldots,x_n]$ generated by the operators of multiplication by $x_i$ and the divided difference ...
- 8,866