کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772997 | 1631062 | 2017 | 69 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The universal DAHA of type (C1â¨,C1) and Leonard pairs of q-Racah type
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The universal DAHA of type (C1â¨,C1) and Leonard pairs of q-Racah type The universal DAHA of type (C1â¨,C1) and Leonard pairs of q-Racah type](/preview/png/5772997.png)
چکیده انگلیسی
A Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Let F denote an algebraically closed field, and fix a nonzero qâF that is not a root of unity. The universal double affine Hecke algebra (DAHA) HËq of type (C1â¨,C1) is the associative F-algebra defined by generators {ti±1}i=03 and relations (i) titiâ1=tiâ1ti=1; (ii) ti+tiâ1 is central; (iii) t0t1t2t3=qâ1. We consider the elements X=t3t0 and Y=t0t1 of HËq. Let V denote a finite-dimensional irreducible HËq-module on which each of X, Y is diagonalizable and t0 has two distinct eigenvalues. Then V is a direct sum of the two eigenspaces of t0. We show that the pair X+Xâ1, Y+Yâ1 acts on each eigenspace as a Leonard pair, and each of these Leonard pairs falls into a class said to have q-Racah type. Thus from V we obtain a pair of Leonard pairs of q-Racah type. It is known that a Leonard pair of q-Racah type is determined up to isomorphism by a parameter sequence (a,b,c,d) called its Huang data. Given a pair of Leonard pairs of q-Racah type, we find necessary and sufficient conditions on their Huang data for that pair to come from the above construction.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 533, 15 November 2017, Pages 14-83
Journal: Linear Algebra and its Applications - Volume 533, 15 November 2017, Pages 14-83
نویسندگان
Kazumasa Nomura, Paul Terwilliger,