A closed formula in the deformed affine nilHecke algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910762373480448 |
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| author | Elias, Ben Juteau, Daniel Young, Benjamin |
| author_facet | Elias, Ben Juteau, Daniel Young, Benjamin |
| contents | There is a q-deformation of the reflection representation of the affine symmetric group, which arises in the quantum geometric Satake equivalence, and in the study of the complex reflection groups $G(m,m,n)$. Demazure operators (often called divided difference operators) act on the polynomial ring of this deformed representation. When $n=3$ we prove an explicit closed formula for the scalar one obtains when applying a degree $-k$ Demazure operator to a monomial of degree $k$. We also prove a simpler formula for the scalar obtained after specializing q to a root of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A closed formula in the deformed affine nilHecke algebra Elias, Ben Juteau, Daniel Young, Benjamin Representation Theory There is a q-deformation of the reflection representation of the affine symmetric group, which arises in the quantum geometric Satake equivalence, and in the study of the complex reflection groups $G(m,m,n)$. Demazure operators (often called divided difference operators) act on the polynomial ring of this deformed representation. When $n=3$ we prove an explicit closed formula for the scalar one obtains when applying a degree $-k$ Demazure operator to a monomial of degree $k$. We also prove a simpler formula for the scalar obtained after specializing q to a root of unity. |
| title | A closed formula in the deformed affine nilHecke algebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.18679 |