Alcove path and Nichols-Woronowicz model of the equivariant $K$-theory of generalized flag varieties
| dc.creator | Lenart, Cristian | |
| dc.creator | Maeno, Toshiaki | |
| dc.date | 2006-07-05 | |
| dc.date | 2006-08-16 | |
| dc.date.accessioned | 2026-07-07T07:18:04Z | |
| dc.date.available | 2026-07-07T07:18:04Z | |
| dc.description | Fomin and Kirillov initiated a line of research into the realization of the cohomology and $K$-theory of generalized flag varieties $G/B$ as commutative subalgebras of certain noncommutative algebras. This approach has several advantages, which we discuss. This paper contains the most comprehensive result in a series of papers related to the mentioned line of research. More precisely, we give a model for the $T$-equivariant $K$-theory of a generalized flag variety $K_T(G/B)$ in terms of a certain braided Hopf algebra called the Nichols-Woronowicz algebra. Our model is based on the Chevalley-type multiplication formula for $K_T(G/B)$ due to the first author and Postnikov; this formula is stated using certain operators defined in terms of so-called alcove paths (and the corresponding affine Weyl group). Our model is derived using a type-independent and concise approach. | |
| dc.identifier | https://arxiv.org/abs/math/0607136 | |
| dc.identifier | http://arxiv.org/abs/math/0607136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114170 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.title | Alcove path and Nichols-Woronowicz model of the equivariant $K$-theory of generalized flag varieties | |
| dc.type | text |