کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6416426 | 1631144 | 2014 | 62 صفحه PDF | دانلود رایگان |
Let F denote an algebraically closed field, and fix a nonzero qâF that is not a root of unity. We consider the q-tetrahedron algebra â q over F. It is known that each finite-dimensional irreducible â q-module of type 1 is a tensor product of evaluation modules. This paper contains a comprehensive description of the evaluation modules for â q. This description includes the following topics. Given an evaluation module V for â q, we display 24 bases for V that we find attractive. For each basis we give the matrices that represent the â q-generators. We give the transition matrices between certain pairs of bases among the 24. It is known that the cyclic group Z4 acts on â q as a group of automorphisms. We describe what happens when V is twisted via an element of Z4. We discuss how evaluation modules for â q are related to Leonard pairs of q-Racah type.
Journal: Linear Algebra and its Applications - Volume 451, 15 June 2014, Pages 107-168