Representations of the Quantum Algebra suq(1,1) and Discrete q-Ultraspherical Polynomials
نویسندگان
چکیده
منابع مشابه
MULTIVARIABLE q-HAHN POLYNOMIALS AS COUPLING COEFFICIENTS FOR QUANTUM ALGEBRA REPRESENTATIONS
We study coupling coefficients for a multiple tensor product of highest weight representations of the SU(1,1) quantum group. These are multivariable generalizations of the q-Hahn polynomials. 2000 Mathematics Subject Classification. 17B37, 33D70, 33D80.
متن کاملA second addition formula for continuous q-ultraspherical polynomials
This paper provides the details of Remark 5.4 in the author’s paper “Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group”, SIAM J. Math. Anal. 24 (1993), 795–813. In formula (5.9) of the 1993 paper a two-parameter class of Askey-Wilson polynomials was expanded as a finite Fourier series with a product of two 3phi2’s as Fourier coefficients. The proof given there use...
متن کامل1 REPRESENTATIONS OF THE q-DEFORMED ALGEBRA U ′ q (so4)
We study the nonstandard q-deformation U ′ q (so 4) of the universal enveloping algebra U (so 4) obtained by deforming the defining relations for skew-symmetric generators of U (so 4). This algebra is used in quantum gravity and algebraic topology. We construct a homomor-phism φ of U ′ q (so 4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra U q (sl 2) ⊗2 and show that...
متن کاملRepresentations and Q-Boson Realization of The Algebra of Functions on The Quantum Group GLq(n)
We present a detailed study of the representations of the algebra of functions on the quantum group GLq(n). A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations of the generators of this algebra. At the end a q-boson realization of the generators of GLq(n) is given.
متن کاملA q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(ĝln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand–Tsetlin character (or q-character). We also apply the qu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2005
ISSN: 1815-0659
DOI: 10.3842/sigma.2005.016