TY - JOUR

T1 - The universal DAHA of type and Leonard triples

AU - Huang, Hau Wen

N1 - Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.

PY - 2020

Y1 - 2020

N2 - Assume that (Formula presented.) is an algebraically closed field and q is a nonzero scalar in (Formula presented.) that is not a root of unity. The universal Askey–Wilson algebra (Formula presented.) is a unital associative (Formula presented.) -algebra generated by A, B, C and the relations state that each of (Formula presented.) is central in (Formula presented.) The universal DAHA (Formula presented.) of type (Formula presented.) is a unital associative (Formula presented.) -algebra generated by (Formula presented.) and the relations state that (Formula presented.) It was given an (Formula presented.) -algebra homomorphism (Formula presented.) that sends (Formula presented.) Therefore, any (Formula presented.) -module can be considered as a (Formula presented.) -module. Let V denote a finite-dimensional irreducible (Formula presented.) -module. In this paper, we show that A, B, C are diagonalizable on V if and only if A, B, C act as Leonard triples on all composition factors of the (Formula presented.) -module V.

AB - Assume that (Formula presented.) is an algebraically closed field and q is a nonzero scalar in (Formula presented.) that is not a root of unity. The universal Askey–Wilson algebra (Formula presented.) is a unital associative (Formula presented.) -algebra generated by A, B, C and the relations state that each of (Formula presented.) is central in (Formula presented.) The universal DAHA (Formula presented.) of type (Formula presented.) is a unital associative (Formula presented.) -algebra generated by (Formula presented.) and the relations state that (Formula presented.) It was given an (Formula presented.) -algebra homomorphism (Formula presented.) that sends (Formula presented.) Therefore, any (Formula presented.) -module can be considered as a (Formula presented.) -module. Let V denote a finite-dimensional irreducible (Formula presented.) -module. In this paper, we show that A, B, C are diagonalizable on V if and only if A, B, C act as Leonard triples on all composition factors of the (Formula presented.) -module V.

KW - Askey–Wilson algebras

KW - Leonard pairs

KW - Leonard triples

KW - double affine Hecke algebras

UR - http://www.scopus.com/inward/record.url?scp=85094146209&partnerID=8YFLogxK

U2 - 10.1080/00927872.2020.1832105

DO - 10.1080/00927872.2020.1832105

M3 - 期刊論文

AN - SCOPUS:85094146209

SN - 0092-7872

VL - 49

SP - 1255

EP - 1273

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -