Fock space representation of the circle quantum group
| Autor: | Francesco Sala, Olivier Schiffmann |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Quantum group
General Mathematics 010102 general mathematics Type (model theory) 01 natural sciences Fock space Combinatorics 17B37 22E65 0103 physical sciences Lie algebra Mathematics - Quantum Algebra FOS: Mathematics Partition (number theory) Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics Representation Theory (math.RT) Mathematics::Representation Theory Quantum Mathematics - Representation Theory Vector space Mathematics |
| DOI: | 10.48550/arxiv.1903.02813 |
| Popis: | In [arXiv:1711.07391] we have defined quantum groups $\mathbf{U}_\upsilon(\mathfrak{sl}(\mathbb{R}))$ and $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1))$, which can be interpreted as continuous generalizations of the quantum groups of the Kac-Moody Lie algebras of finite, respectively affine type $A$. In the present paper, we define the Fock space representation $\mathcal{F}_{\mathbb{R}}$ of the quantum group $\mathbf{U}_\upsilon(\mathfrak{sl}(\mathbb{R}))$ as the vector space generated by real pyramids (a continuous generalization of the notion of partition). In addition, by using a variant of the "folding procedure" of Hayashi-Misra-Miwa, we define an action of $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1))$ on $\mathcal{F}_{\mathbb{R}}$. Comment: 25 pages; v2: 29 pages, Final version published in IMRN |
| Databáze: | OpenAIRE |
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