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arXiv · 2512.15272

Fused permutations algebras and degenerate affine Hecke algebras

Yoann Demesmay
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Abstract

This paper gives an algebraic presentation of an algebra called the fused permutations algebra in the one-boundary case. It is obtained through a detailed study of the degenerate cyclotomic Hecke algebra. In particular, we prove that the fused permutations algebra is a quotient of the degenerate cyclotomic affine Hecke algebra, and we also describe a basis combinatorially in terms of signed permutations with avoiding patterns. In order to understand this quotient, we study the primitive idempotents of this degenerate cyclotomic affine Hecke algebra.

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BibTeXRIS

Yoann Demesmay. 2025-12-17. Fused permutations algebras and degenerate affine Hecke algebras. https://arxiv.org/abs/2512.15272

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