An Algebraic Characterization of the Affine Canonical Basis
| dc.creator | Beck, Jonathan | |
| dc.creator | Chari, Vyjayanthi | |
| dc.creator | Pressley, Andrew | |
| dc.date | 1998-08-13 | |
| dc.date.accessioned | 2026-07-07T05:25:42Z | |
| dc.date.available | 2026-07-07T05:25:42Z | |
| dc.description | The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the explicit construction (via the braid group action) of a lattice over $\bz[q^{-1}]$. This allows the algebraic characterization of the canonical basis as a certain bar-invariant basis of $\cl$. Here we present a similar algebraic characterization of the affine canonical basis. Our construction is complicated by the need to introduce basis elements to span the ``imaginary'' subalgebra which is fixed by the affine braid group. Once the basis is found we construct a PBW-type basis whose $\bz[q^{-1}]$-span reduces to a ``crystal'' basis at $q=\infty,$ with the imaginary component given by the Schur functions. | |
| dc.identifier | https://arxiv.org/abs/math/9808060 | |
| dc.identifier | http://arxiv.org/abs/math/9808060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77282 | |
| dc.subject | Quantum Algebra | |
| dc.title | An Algebraic Characterization of the Affine Canonical Basis | |
| dc.type | text |