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## 摘要

Assume that F is an algebraically closed field with characteristic zero. The universal Racah algebra ℜ is a unital associative F-algebra defined by generators and relations. The generators are A,B,C,D and the relations state that [A,B]=[B,C]=[C,A]=2D and each of [A,D]+AC−BA,[B,D]+BA−CB,[C,D]+CB−AC is central in ℜ. The universal additive DAHA (double affine Hecke algebra) H of type (C_{1}^{∨},C_{1}) is a unital associative F-algebra generated by t_{0},t_{1},t_{0}^{∨},t_{1}^{∨} and the relations state that t_{0}+t_{1}+t_{0}^{∨}+t_{1}^{∨}=−1 and each of t_{0}^{2},t_{1}^{2},t_{0}^{∨2},t_{1}^{∨2} is central in H. Each H-module is an ℜ-module by pulling back via the algebra homomorphism ℜ→H given by [Formula presented] Let V denote any finite-dimensional irreducible H-module. The set of ℜ-submodules of V forms a lattice under the inclusion partial order. We classify the lattices that arise by this construction. As a consequence, the ℜ-module V is completely reducible if and only if t_{0} is diagonalizable on V.

原文 | ???core.languages.en_GB??? |
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文章編號 | 106653 |

期刊 | Journal of Pure and Applied Algebra |

卷 | 225 |

發行號 | 8 |

DOIs | |

出版狀態 | 已出版 - 8月 2021 |

## 指紋

深入研究「Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type (C_{1}

^{∨},C

_{1})」主題。共同形成了獨特的指紋。

## 專案

- 1 已完成