Lie algebras and recurrence relations III:q-analogs and quantized algebras

1990 ◽  
Vol 19 (3) ◽  
pp. 207-251 ◽  
Author(s):  
Philip Feinsilver
Keyword(s):  
Lie Algebras ◽  
Recurrence Relations

Lie Algebras and Recurrence Relations II

1989 ◽  
pp. 163-179 ◽  
Author(s):  
Philip Feinsilver
Keyword(s):  
Lie Algebras ◽  
Recurrence Relations

scholarly journals A RECURRENCE RELATION FOR CHARACTERS OF HIGHEST WEIGHT INTEGRABLE MODULES FOR AFFINE LIE ALGEBRAS

2007 ◽  
Vol 09 (02) ◽  
pp. 121-133 ◽  
Author(s):  
WILLIAM J. COOK ◽  
HAISHENG LI ◽  
KAILASH C. MISRA
Keyword(s):  
Recurrence Relation ◽  
Lie Algebras ◽  
Vertex Operator ◽  
Recurrence Relations ◽  
Operator Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Irreducible Modules ◽  
Level 1 ◽  
Integrable Modules

Using certain results for the vertex operator algebras associated with affine Lie algebras, we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an affine Lie algebra. As an application we show that in the simply-laced level 1 case, these recurrence relations give the known characters, whose principal specializations naturally give rise to some multisum Macdonald identities.

scholarly journals New realizations of algebras of the Askey–Wilson type in terms of Lie and quantum algebras

2020 ◽  
pp. 2150002
Author(s):  
Nicolas Crampé ◽  
Dounia Shaaban Kabakibo ◽  
Luc Vinet
Keyword(s):  
Orthogonal Polynomials ◽  
Lie Algebras ◽  
Recurrence Relations ◽  
Rational Functions ◽  
The Other ◽  
Quantum Algebras ◽  
Casimir Element ◽  
Usual Representation ◽  
Racah Algebra

The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras [Formula: see text] or [Formula: see text]. A new realization of the Racah algebra in terms of the Lie algebras [Formula: see text] or [Formula: see text] is also given. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey–Wilson (or Racah) algebra becomes diagonal in the usual representation of the quantum algebras whereas the second one is tridiagonal. This allows us to recover easily the recurrence relations of the associated orthogonal polynomials of the Askey scheme. These realizations involve rational functions of the Cartan generator of the quantum algebras, where they are linear with respect to the other generators and depend on the Casimir element of the quantum algebras.

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras

Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials

2018 ◽  
Vol 11 (3) ◽  
pp. 29-39
Author(s):  
E. I. Jafarov ◽  
A. M. Jafarova ◽  
S. M. Nagiyev
Keyword(s):  
Recurrence Relations ◽  
Pollaczek Polynomials

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.

The rigidity of some solvable Lie algebras

2018 ◽  
Vol 2018 (2) ◽  
pp. 43-49
Author(s):  
R.K. Gaybullaev ◽  
Kh.A. Khalkulova ◽  
J.Q. Adashev
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras
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