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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 …
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 …
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 …
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 …