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Evaluation modules ...
Evaluation modules for the q-tetrahedron algebra
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- Ito, Tatsuro (författare)
- Kanazawa University
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- Rosengren, Hjalmar, 1972 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics
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- Terwilliger, Paul (författare)
- University of Wisconsin Madison
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(creator_code:org_t)
- Elsevier BV, 2014
- 2014
- Engelska.
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Ingår i: Linear Algebra and Its Applications. - : Elsevier BV. - 0024-3795. ; 451, s. 107-168
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Abstract
Ämnesord
Stäng
- Let F denote an algebraically closed field, and fix a nonzero q∈F that is not a root of unity. We consider the q-tetrahedron algebra ⊠q over F. It is known that each finite-dimensional irreducible ⊠q-module of type 1 is a tensor product of evaluation modules. This paper contains a comprehensive description of the evaluation modules for ⊠q. This description includes the following topics. Given an evaluation module V for ⊠q, we display 24 bases for V that we find attractive. For each basis we give the matrices that represent the ⊠q-generators. We give the transition matrices between certain pairs of bases among the 24. It is known that the cyclic group $\Z_4$ acts on ⊠q as a group of automorphisms. We describe what happens when V is twisted via an element of $\Z_4$. We discuss how evaluation modules for ⊠q are related to Leonard pairs of q-Racah type.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Leonard pair
- Tetrahedron algebra
- Equitable presentation
- Equitable presentation; Leonard pair; Tetrahedron algebra
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