Elliptic Quantum Groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910452736327680 |
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| author | Konno, Hitoshi |
| author_facet | Konno, Hitoshi |
| contents | We expose the elliptic quantum groups in the Drinfeld realization associated with both the affine Lie algebra \g and the toroidal algebra \g_tor. There the level-0 and level \not=0 representations appear in a unified way so that one can define the vertex operators as intertwining operators of them. The vertex operators are key for many applications such as a derivation of the elliptic weight functions, integral solutions of the (elliptic) q-KZ equation and a formulation of algebraic analysis of the elliptic solvable lattice models. Identifying the elliptic weight functions with the elliptic stable envelopes we make a correspondence between the level-0 representation of the elliptic quantum group and the equivariant elliptic cohomology. We also emphasize a characterization of the elliptic quantum groups as $q$-deformations of the W-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elliptic Quantum Groups Konno, Hitoshi Representation Theory High Energy Physics - Theory Algebraic Geometry Quantum Algebra 17B37 We expose the elliptic quantum groups in the Drinfeld realization associated with both the affine Lie algebra \g and the toroidal algebra \g_tor. There the level-0 and level \not=0 representations appear in a unified way so that one can define the vertex operators as intertwining operators of them. The vertex operators are key for many applications such as a derivation of the elliptic weight functions, integral solutions of the (elliptic) q-KZ equation and a formulation of algebraic analysis of the elliptic solvable lattice models. Identifying the elliptic weight functions with the elliptic stable envelopes we make a correspondence between the level-0 representation of the elliptic quantum group and the equivariant elliptic cohomology. We also emphasize a characterization of the elliptic quantum groups as $q$-deformations of the W-algebras. |
| title | Elliptic Quantum Groups |
| topic | Representation Theory High Energy Physics - Theory Algebraic Geometry Quantum Algebra 17B37 |
| url | https://arxiv.org/abs/2405.11193 |