Finite-dimensional modules of the universal Askey–Wilson algebra and DAHA of type $$(C_1^\vee ,C_1)$$
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DOI: 10.1007/s11005-021-01422-0
Abstract: Assume that $\mathbb F$ is an algebraically closed field and let $q$ denote a nonzero scalar in $\mathbb F$ that is not a root of unity. The universal Askey--Wilson algebra $\triangle_q$ is a unital associative… read more here.
Keywords: algebra; mathfrak; universal askey; askey wilson ... See more keywords
The q-Higgs and Askey–Wilson algebras
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DOI: 10.1016/j.nuclphysb.2019.114632
Abstract: Abstract A q-analogue of the Higgs algebra, which describes the symmetry properties of the harmonic oscillator on the 2-sphere, is obtained as the commutant of the o q 1 / 2 ( 2 ) ⊕… read more here.
Keywords: wilson; algebra; wilson algebras; higgs askey ... See more keywords
Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
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DOI: 10.1016/j.nuclphysb.2019.114824
Abstract: Abstract An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in… read more here.
Keywords: wilson; bethe ansatz; heun askey; askey wilson ... See more keywords
The Askey–Wilson algebra and its avatars
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DOI: 10.1088/1751-8121/abd783
Abstract: The original Askey–Wilson algebra introduced by Zhedanov encodes the bispectrality properties of the eponym polynomials. The name Askey–Wilson algebra is currently used to refer to a variety of related structures that appear in a large… read more here.
Keywords: algebra avatars; algebra; wilson algebra; askey wilson ... See more keywords
Askey–Wilson polynomial and genus-two skein module
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DOI: 10.1088/1751-8121/ae144a
Abstract: Based on the q-difference operators for the genus-two skein algebra, we show the correspondence between the reduced Askey–Wilson polynomials and the skein module of the genus-2 handlebody. read more here.
Keywords: askey wilson; genus two; two skein; wilson polynomial ... See more keywords