Positivity in $T$-Equivariant $K$-theory of partial flag varieties associated to Kac-Moody groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912447771705344 |
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| author | Compton, Joseph Kumar, Shrawan |
| author_facet | Compton, Joseph Kumar, Shrawan |
| contents | We prove sign-alternation of the product structure constants in the basis dual to the basis consisting of the structure sheaves of Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the partial flag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic subgroup of finite type. This extends the previous work of Kumar from $G/B$ to $G/P$. When $G$ is of finite type, i.e., it is a semisimple group, then it was proved by Anderson-Griffeth-Miller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03353 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positivity in $T$-Equivariant $K$-theory of partial flag varieties associated to Kac-Moody groups Compton, Joseph Kumar, Shrawan Algebraic Geometry Algebraic Topology Group Theory K-Theory and Homology 19L47, 20G44, 14M15 We prove sign-alternation of the product structure constants in the basis dual to the basis consisting of the structure sheaves of Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the partial flag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic subgroup of finite type. This extends the previous work of Kumar from $G/B$ to $G/P$. When $G$ is of finite type, i.e., it is a semisimple group, then it was proved by Anderson-Griffeth-Miller. |
| title | Positivity in $T$-Equivariant $K$-theory of partial flag varieties associated to Kac-Moody groups |
| topic | Algebraic Geometry Algebraic Topology Group Theory K-Theory and Homology 19L47, 20G44, 14M15 |
| url | https://arxiv.org/abs/2304.03353 |