Equivariant K-theory of the space of partial flags
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916760613027840 |
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| author | Arkhipov, Sergey Mazin, Mikhail |
| author_facet | Arkhipov, Sergey Mazin, Mikhail |
| contents | We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a ``$q=0$'' version of the affine quantum group of $\mathfrak{gl}_n.$ We then use the convolution product on the equivariant $K$-theory of varieties of pairs of partial flags in a $d$-dimensional vector space $V$ to define affine $0$-Schur algebras ${\mathbb S}_0^{\operatorname{aff}}(n,d)$ and to prove that for every $d$ there exists a surjective homomorphism from $\mathfrak{U}_n$ to ${\mathbb S}_0^{\operatorname{aff}}(n,d).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_05184 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equivariant K-theory of the space of partial flags Arkhipov, Sergey Mazin, Mikhail Representation Theory Combinatorics Quantum Algebra 20G42, 20G43, 17B37 We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a ``$q=0$'' version of the affine quantum group of $\mathfrak{gl}_n.$ We then use the convolution product on the equivariant $K$-theory of varieties of pairs of partial flags in a $d$-dimensional vector space $V$ to define affine $0$-Schur algebras ${\mathbb S}_0^{\operatorname{aff}}(n,d)$ and to prove that for every $d$ there exists a surjective homomorphism from $\mathfrak{U}_n$ to ${\mathbb S}_0^{\operatorname{aff}}(n,d).$ |
| title | Equivariant K-theory of the space of partial flags |
| topic | Representation Theory Combinatorics Quantum Algebra 20G42, 20G43, 17B37 |
| url | https://arxiv.org/abs/2205.05184 |