Last edited by Goltishakar

Wednesday, July 22, 2020 | History

2 edition of **On quantum groups, hypergroups and q-special functions** found in the catalog.

On quantum groups, hypergroups and q-special functions

P. G. A. Floris

- 317 Want to read
- 34 Currently reading

Published
**1995**
.

Written in English

- Quantum groups.,
- Hypergroups.,
- Functions, Special.,
- q-series.

**Edition Notes**

Statement | P.G.A. Floris. |

The Physical Object | |
---|---|

Pagination | viii, 111 p. |

Number of Pages | 111 |

ID Numbers | |

Open Library | OL19438526M |

A great introduction to the exciting new world of quantum computing. William Wheeler Learn Quantum Computing with Python and Q# demystifies quantum computing. Using Python and the new quantum programming language Q#, you’ll build your own quantum simulator and apply quantum programming techniques to real-world examples including cryptography and chemical analysis. Moreover, group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal : Hardcover.

Special functions and q-series are very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, This work presents the subject and its applications. The book contains some results about q-special functions in connection with quantum groups: in particular on q-analogues of Clebsch-Gordan coefficients and Racah coefficients, and about q-hypergeometric functions in connection with induced representations of the quantized universal enveloping algebra for U(3).

The lecture notes contains an introduction to quantum groups, q-special functions and their interplay. After generalities on Hopf algebras, orthogonal polynomials and basic hypergeometric series we work out the relation between the quantum SU(2) group and the Askey-Wilson polynomials out in . On application side, possible topics are: classical and quantum integrable models with quantum group invariance; the applications of quantum groups in different (2+1) quantum gravity contexts (like combinatorial quantisation, state sum models or spin foams); and quantum kinematical groups and their noncommutative spacetimes in connection with.

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Alternatively, the quantum group U q (G) can be regarded as an algebra over the field C(q), the field of all rational functions of an indeterminate q over C. Similarly, the quantum group U q (G) can be regarded as an algebra over the field Q(q), the field of all rational functions of an indeterminate q over Q (see below in the section on quantum groups at q = 0).

Gel/fand pairs of quantum groups, hypergroups and q-special functions LEONID VAINERMAN Central limit theorems for Jacobi hypergroups MICHAEL VOIT Finite commutative hyper groups and applications from group theory to conformal field theory N.

WILDBERGER Kolmogorov's three series theorem on one-dimensional hypergroups. Quantum groups are not groups at all, but special kinds of Hopf algebras of which the most important are closely related to Lie groups and play a central role in the statistical and wave mechanics of Baxter and Yang.

Those occurring physically can be studied as essentially algebraic and closely related to the deformation theory of algebras (commutative, Lie, Hopf, and so on).

Applications of Hypergroups and Related Measure Algebras About this Title. William C. Connett, Marc-Olivier Gebuhrer and Alan L. Schwartz, Editors. Publication: Contemporary Mathematics Publication Year Volume ISBNs: (print); (online)Cited by: 8.

The compact quantum hypergroups, as developed by Chapovsky and Vainerman in [2], and studied further (cf. e.g. [19] and [9]), should be a special case of these locally compact quantum hypergroups, just as the hypergroups and q-special functions book quantum groups, as developed by Woronowicz (cf.

[25] and [26], see also [17]) are a special case of the general locally compact Cited by: Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected] There has been revived interest in recent years in the study of special functions.

Many of the latest hypergroups and q-special functions book in the field were inspired by the works of R. Askey and colleagues on basic hypergeometric series and I. Macdonald on orthogonal polynomials related to root systems.

Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and. A study, with extensive examples, of Gel'fand pairs of quantum groups, related ^-special functions and their connection with hypergroups can be found in [V].

The purpose of this paper is to present two criteria for the above-mentioned Gel'fand property, analogous to the. From the introduction: `The most important single thing about this conference was that it brought together for the first time represenatives of all major groups of users of hypergroups.

[They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This. The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo inor variations thereof.

The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. the nal section we consider Fourier algebras of hypergroups arising from compact quantum groups G, and in particular, establish a completely isometric isomorphism with the center of the quantum group algebra for compact G of Kac type.

1Introduction The Fourier algebra A(G) of a locally compact group Gis a central object in abstract harmonic. of a generalized quantum Gelfand pair, where the role of the quantum subgroup is taken over by a two-sided coideal in the dual Hopf algebra. The paper starts with a review of compact quantum groups, with an approach in terms of so-called CQG algebras.

The paper concludes with some examples of hypergroups thus obtained. Introduction. An underlying theme of the conference was hypergroups, the the ory of wh ich has developed and been found useful in fields as diverse as special functions, differential equations, probability theory, representa tion theory, measure theory, Hopf algebras and quantum groups.

The series of these meetings inaugurated in by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum.

Algebraic quantum hypergroups imbedded in algebraic quantum groups Kenny De Commer Dipartimento di Matematica, Universit a degli Studi di Roma Tor Vergata Via della Ricerca Scienti ca 1, Roma, Italy e-mail: [email protected] Abstract We show that for any -algebraic quantum group, the space of invariants for the square of the antipode.

The aim of this article is to study the q-Laplace operator and q-harmonic polynomials on the quantum complex vector space generated by elements z i,w i, i=1,2,n, on which the quantum group GL q (n) [or U q (n)] acts.

This method generalizes the scheme of the construction of ordinary DJS-hypergroups with the use of orbital morphisms [9] and includes the construction of double cosets for quantum groups [6, 7.

A compact quantum hypergroup is a unital C * -algebra equipped with a completely positive coassociative coproduct. The most important examples of such a. of locally compact quantum groups a la Kustermans and Vaes in Chapter 6.

Chapter 7 is then devoted to the main example of such a locally compact quantum group, namely for the normaliser of SU(1,1) in SL(2,C). This construction is based on special functions, and we recall in Chapter 4 some ideas that have led to this construction.

$, ISBN ; Vol. 3: Classical and quantum groups and special functions, vol. 75,xx+ pp., $, ISBN X Review by Erik Koelink and Tom H. Koornwinder The book under review deals with the interplay between two branches of mathematics, namely representation theory of groups and the theory of special functions.

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops.Quantum groups are used to define q-special functions.

The Casimir operatorsof a variation of SU q(2) and E q(2) are derived. The proposed q-associated Legendreand q-Bessel functions are the eigenfunctions of the Casimirs.

The results differfrom ordinary q-special functions, but this is expected since the q-generalizationis not unique. Get this from a library! Applications of hypergroups and related measure algebras: a Joint Summer Research Conference on Applications of Hypergroups and Related Measure Algebras, July August 6,Seattle, Washington.

[William C Connett; Marc-Olivier Gebuhrer; Alan L Schwartz;] -- "Hypergroups occur in a wide variety of contexts, and mathematicians the world over .