Yangians, quantum loop algebras and abelian difference equations
| Autor: | Gautam, S., Toledano-Laredo, V. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Journal of the American Mathematical Society 29 (2016), 775-824 |
| Druh dokumentu: | Working Paper |
| Popis: | Let g be a complex, semisimple Lie algebra, and Y_h(g) and U_q(Lg) the Yangian and quantum loop algebra of g. Assuming that h is not a rational number and that q=exp(i \pi h), we construct an equivalence between the finite-dimensional representations of U_q(Lg) and an explicit subcategory of those of Y_h(g) defined by choosing a branch of the logarithm. This equivalence is governed by the monodromy of the abelian additive difference equations defined by the commuting fields of Y_h(g). Our results are compatible with q-characters, and apply more generally to a symmetrisable Kac-Moody algebra g, in particular to affine Yangians and quantum toroidal algebras. In this generality, they yield an equivalence between the representations of Y_h(g) and U_q(Lg) whose restriction to g and U_q(g) respectively are integrable and in category O. Comment: Minor typos corrected. Final version. To appear in JAMS. 55 pages |
| Databáze: | arXiv |
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