Tensor ideals in the category of tilting modules
| dc.creator | Ostrik, V. | |
| dc.date | 1996-11-27 | |
| dc.date | 1997-06-27 | |
| dc.date.accessioned | 2026-07-07T09:04:58Z | |
| dc.date.available | 2026-07-07T09:04:58Z | |
| dc.description | We study the tensor category $\cQ$ of tilting modules over a quantum group $U_q$ with divided powers. The set $X_+$ of dominant weights is a union of closed alcoves $\oC_w$ numbered by the elements $w\in W^f$ of a certain subset of affine Weyl group $W$. G.Lusztig and N.Xi defined a partition of $W^f$ into canonical right cells and the right order $\le_R$ on the set of cells. For a cell $A\subset W^f$ we consider a full subcategory $\cQ_{<A}$ formed by direct sums of tilting modules $Q(λ)$ with highest weights $λ\in \bigcup_{w\in B<_RA} \oC_w$. We prove that $\cQ_{<A}$ is a tensor ideal in $\cQ$, generalizing H.Andersen's Theorem about the ideal of negligible modules which in our notations is nothing else then $\cQ_{<\{ e\}}$. The proof is an application of a recent result by W.Soergel who has computed the characters of tilting modules. | |
| dc.description | 9 pages. Essential simplifications in proofs are made | |
| dc.identifier | https://arxiv.org/abs/q-alg/9611033 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9611033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149573 | |
| dc.subject | Quantum Algebra | |
| dc.title | Tensor ideals in the category of tilting modules | |
| dc.type | text |