On quantum $K$-groups of partial flag manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866911617156907008 |
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| author | Kato, Syu |
| author_facet | Kato, Syu |
| contents | We show that the equivariant small quantum $K$-group of a partial flag manifold is a quotient of that of the full flag manifold in a way that respects the Schubert classes. This is a $K$-theoretic analogue of the parabolic version of Peterson's theorem [Lam-Shimozono, Acta Math. {\bf 204} (2010)] that exhibits a different behavior from the case of quantum cohomology. Our quotient maps send some of the Novikov variables to $1$, and the geometric meaning of this specialization is unclear in quantum $K$-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_09343 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On quantum $K$-groups of partial flag manifolds Kato, Syu Algebraic Geometry Quantum Algebra Representation Theory We show that the equivariant small quantum $K$-group of a partial flag manifold is a quotient of that of the full flag manifold in a way that respects the Schubert classes. This is a $K$-theoretic analogue of the parabolic version of Peterson's theorem [Lam-Shimozono, Acta Math. {\bf 204} (2010)] that exhibits a different behavior from the case of quantum cohomology. Our quotient maps send some of the Novikov variables to $1$, and the geometric meaning of this specialization is unclear in quantum $K$-theory. |
| title | On quantum $K$-groups of partial flag manifolds |
| topic | Algebraic Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/1906.09343 |