Support varieties for quantum groups
| dc.creator | Ostrik, V. | |
| dc.date | 1997-11-12 | |
| dc.date | 1998-02-09 | |
| dc.date.accessioned | 2026-07-07T05:57:41Z | |
| dc.date.available | 2026-07-07T05:57:41Z | |
| dc.description | For any module $M$ over small quantum group one defines the support variety using construction from the theory of restricted Lie algebras. It is a closed conical subset of nilpotent cone of the corresponding Lie algebra. If module $M$ is a module over the quantum group $U_ξ$ with divided powers then its support variety is invariant under the action of the corresponding algebraic group. In this case we relate codimension $2a$ of the support variety of $M$ in nilpotent cone and dimension of $M$. Namely, we prove that $\dim M$ is `almost' divisible by $l^a$. Further, we give an a priori estimate for support variety of a module in a given linkage class. We compute the support varieties for Weyl modules. Also we compute the support varieties for tilting modules over quantum $SL_n$ and verify in this case Humphreys' Conjecture which relates support varieties of tilting modules with Lusztig's bijection between nilpotent orbits and two-sided cells in the affine Weyl group. | |
| dc.description | 11 pages. The proof of the Theorem 4.5 is extended in order to avoid a gap found by J.C.Jantzen | |
| dc.identifier | https://arxiv.org/abs/q-alg/9711008 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9711008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/88076 | |
| dc.subject | Quantum Algebra | |
| dc.title | Support varieties for quantum groups | |
| dc.type | text |