The PBW Filtration, Demazure Modules and Toroidal Current Algebras
| dc.creator | Feigin, Evgeny | |
| dc.date | 2008-06-30 | |
| dc.date | 2008-10-14 | |
| dc.date.accessioned | 2026-07-07T10:09:19Z | |
| dc.date.available | 2026-07-07T10:09:19Z | |
| dc.description | Let $L$ be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra $\hat{\mathfrak g}$. The $m$-th space $F_m$ of the PBW filtration on $L$ is a linear span of vectors of the form $x_1... x_lv_0$, where $l\le m$, $x_i\in \hat{\mathfrak g}$ and $v_0$ is a highest weight vector of $L$. In this paper we give two descriptions of the associated graded space $L^{\rm gr}$ with respect to the PBW filtration. The "top-down" description deals with a structure of $L^{\rm gr}$ as a representation of the abelianized algebra of generating operators. We prove that the ideal of relations is generated by the coefficients of the squared field $e_θ(z)^2$, which corresponds to the longest root $θ$. The "bottom-up" description deals with the structure of $L^{\rm gr}$ as a representation of the current algebra ${\mathfrak g}\otimes {\mathbb C}[t]$. We prove that each quotient $F_m/F_{m-1}$ can be filtered by graded deformations of the tensor products of $m$ copies of ${\mathfrak g}$. | |
| dc.description | This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0806.4851 | |
| dc.identifier | http://arxiv.org/abs/0806.4851 | |
| dc.identifier | SIGMA 4 (2008), 070, 21 pages | |
| dc.identifier | doi:10.3842/SIGMA.2008.070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171283 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | The PBW Filtration, Demazure Modules and Toroidal Current Algebras | |
| dc.type | text |