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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.

6 votes

Super mixed Hodge structures?

I am not sure this is relevant to you, and you may know this already, but in the theory of monodromic ("exponential") mixed Hodge structures, there is a very natural (even) square root of the Tate mot …
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2 votes

Homogeneous components of Cox RIngs

The answer to all these questions is no. Let $X=F_1$, the first Hirzebruch surface. Let $D_0$ be a fibre of the projection to ${\mathbb P}^1$. Let $D_{-1}$ be the "negative" section of this projection …
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4 votes

Algebra of regular functions on the quadratic cone and SU(2) representations

Apply the Borel-Weil theorem to the Lie group $G={\rm SL}_2({\mathbb C})$, with Borel $B$, the complexification of ${\rm SU}(2)$. The flag variety $G/B={\mathbb P}^1$, and we have $V_m=\Gamma({\mathb …
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1 vote
Accepted

Generating function for $t$-residues of partitions using Heisenberg + $\hat{sl_t}$ represent...

Denote by $\tilde{\mathcal F}$ the Fock space representation of $\widehat{sl}_t$. In fact it is even a $\widehat{gl}_t$-module, and as such irreducible. Now \begin{equation}\widehat{gl}_t= \widehat{sl …
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