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http://dx.doi.org/10.14317/jami.2022.1137

LEONARD PAIRS GENERATED FROM Uq(sl2)  

ALQDERAT, AMANI (Ministry of Education)
ALNAJJAR, HASAN (Department of Mathematics, College of Sciences, the University of Jordan)
Publication Information
Journal of applied mathematics & informatics / v.40, no.5_6, 2022 , pp. 1137-1150 More about this Journal
Abstract
Consider the quantum algebra Uq(sl2) over field 𝓕 (char(𝓕) = 0) with equitable generators x±1, y and z, where q is fixed nonzero, not root of unity scalar in 𝓕. Let V denote a finite dimensional irreducible module for this algebra. Let Λ ∈ End(V), and let {A1, A2, A3} = {x, y, z}. First we show that if Λ, A1 is a Leonard pair, then this Leonard pair have four types, and we show that for each type there exists a Leonard pair Λ, A1 in which Λ is a linear combination of 1, A2, A3, A2A3. Moreover, we use Λ to construct 𝚼 ∈ Uq(sl2) such that 𝚼, A-11 is a Leonard pair, and show that 𝚼 = I + A1Φ + A1ΨA1 where Φ and Ψ are linear combination of 1, A2, A3.
Keywords
Finite-dimensional $U_q(sl_2)$-modules; standard eigenbasis; Leonard pairs;
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Times Cited By KSCI : 1  (Citation Analysis)
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