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Abstract
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 (C1∨,C1) is a unital associative F-algebra generated by t0,t1,t0∨,t1∨ and the relations state that t0+t1+t0∨+t1∨=−1 and each of t02,t12,t0∨2,t1∨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 t0 is diagonalizable on V.
Original language | English |
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Article number | 106653 |
Journal | Journal of Pure and Applied Algebra |
Volume | 225 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2021 |
Keywords
- Additive DAHA
- Irreducible modules
- Racah algebras
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Dive into the research topics of 'Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type (C1∨,C1)'. Together they form a unique fingerprint.Projects
- 1 Finished
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The Unversial Racah Algebra and Its Applications(4/4)
Huang, H.-W. (PI)
1/08/20 → 31/07/21
Project: Research