On the decomposition numbers of the Hecke algebra of type $D_n$ when $n$ is even
| dc.creator | Hu, Jun | |
| dc.date | 2008-09-09 | |
| dc.date | 2008-12-17 | |
| dc.date.accessioned | 2026-07-07T12:13:17Z | |
| dc.date.available | 2026-07-07T12:13:17Z | |
| dc.description | Let $n\geq 4$ be an even integer. Let $K$ be a field with $\cha K\neq 2$ and $q$ an invertible element in $K$ such that $\prod_{i=1}^{n-1}(1+q^i)\neq 0$. In this paper, we study the decomposition numbers over $K$ of the Iwahori--Hecke algebra $\HH_q(D_n)$ of type $D_n$. We obtain some equalities which relate its decomposition numbers with certain Schur elements and the decomposition numbers of various Iwahori--Hecke algebras of type $A$ with the same parameter $q$. When $\cha K=0$, this completely determine all of its decomposition numbers. The main tools we used are the Morita equivalence theorem established in \cite{Hu1} and certain twining character formulae of Weyl modules over a tensor product of two $q$-Schur algebras. | |
| dc.description | corrected some typos | |
| dc.identifier | https://arxiv.org/abs/0809.1690 | |
| dc.identifier | http://arxiv.org/abs/0809.1690 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210795 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B37; 20G42; 20G15 | |
| dc.title | On the decomposition numbers of the Hecke algebra of type $D_n$ when $n$ is even | |
| dc.type | text |