| Autor: |
Evgeny Feigin |
| Jazyk: |
angličtina |
| Rok vydání: |
2008 |
| Předmět: |
|
| Zdroj: |
Symmetry, Integrability and Geometry: Methods and Applications, Vol 4, p 070 (2008) |
| Druh dokumentu: |
article |
| ISSN: |
1815-0659 |
| DOI: |
10.3842/SIGMA.2008.070 |
| Popis: |
Let L be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra ^g. The m-th space F_m of the PBW filtration on L is a linear span of vectors of the form x_1dots x_lv_0, where l ≤ m, x_i in ^g and v_0 is a highest weight vector of L. In this paper we give two descriptions of the associated graded space L^{gr} with respect to the PBW filtration. The ''top-down'' description deals with a structure of L^{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^{gr} as a representation of the current algebra g otimes 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 g. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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