Fused permutations algebras and degenerate affine Hecke algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911324222521344 |
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| author | Demesmay, Yoann |
| author_facet | Demesmay, Yoann |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fused permutations algebras and degenerate affine Hecke algebras Demesmay, Yoann Representation Theory Mathematical Physics 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. |
| title | Fused permutations algebras and degenerate affine Hecke algebras |
| topic | Representation Theory Mathematical Physics |
| url | https://arxiv.org/abs/2512.15272 |