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arXiv · 2412.18679

A closed formula in the deformed affine nilHecke algebra

Ben Elias·Daniel Juteau·Benjamin Young
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Abstract

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.

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Ben Elias, Daniel Juteau, Benjamin Young. 2024-12-24. A closed formula in the deformed affine nilHecke algebra. https://arxiv.org/abs/2412.18679

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