On Models of the Lie Algebra Gu,v and Euler Integral Transformation
DOI:
https://doi.org/10.18311/jims/2024/32906Keywords:
Lie Algebras, Lie Groups, Euler Integral Transformation, Generating Functions, Recurrence Relations.Abstract
In this study, we framed two variable and three variable models of the irreducible representations of the Lie Algebra Gu,v. The two variable models are then transmuted in terms of difference-differential operators using the Euler integral transformation, whereas the three variable models are transmuted in terms of difference-differential operators using the two-fold Euler integral transformation. Then, various recurrence relations and generating functions are obtained using these models.
Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 S. Yadav, Shaifali Thakur
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
R. Chakrabarti and R.Jagannathan, A (p,q)-oscillator realization of two parameter quantum algebras, Journal of Physics A: A Mathematical and General, Vol. 24(13), (1991) 711–718.
G. Gasper and M. Rahman,Basic Hypergeometric Series Second Edition, Cambridge University Press, 2004.
S. Khan, Harmonic oscillator group and Laguerre 2D polynomials, Rep. Math. Phys. 52 (2003) 227-–233.
S. Khan, Certain properties of some special functions of two variables and two indices, Integral Transforms Spec. Funct. 15 (4) (2004) 331-–336.
S. Khan, M. A. Pathan, Lie theoretic generating relations of Hermite 2D polynomials, J. Comput. Appl. Math. 160 (2003) 139—146.
S. Khan, G. Yasmin, Lie-theoretic generating relations of two variable Laguerre polynomials, Rep. Math. Phys. 51 (2003) 1-–7.
H. L. Manocha, Lie algebras of Difference -differential operators and Appell Functions F1, Journal of Mathematical Analysis and Applications, 138, (1989) 491–510.
W. Miller, Lie theory and Special functions, Mathematics in Science and Engineering 43, Academic Press, 1968.
W. Miller, Jr., Symmetry and Separation of Variables, Addison-Wesley, Reading, Mass.,1977.
E. D. Rainville, Special Functions, Macmillian, New York,1960.
Mumtaz Riyasat, Subuhi Khan and Mehnaaz Haneef, Generalized 2D extension of the q-bessel function polynomials, Reports on Mathematical Physics, Vol.90 (1), (2022), 63–80.
Vivek Sahai, On certain models of irreducible representations of sl(2, C) and Euler integral transformation, Indian J. pure appl. Math.,26(12), (1995) 1177 – 1189.
Vivek Sahai and Shalini Srivastava, On models of Lie algebra G⊬,⊮ and Euler integral transformation, J. Indian Math Soc. 71(2004), 1–4.
Vivek Sahai and Sarasvati Yadav, On models of certain p,q-algebra representations: The quantum Euclidean algebra Ep,q(2), Journal of Mathematical Analysis and Applications, 338 (2008) 1043–1053.
Vivek Sahai and Sarasvati Yadav, On models of certain p,q-algebra representations: The p,q-oscillator algebra, Journal of Mathematical Physics, 49, 053504 (2008) 12pages.
Vivek Sahai and Sarasvati Yadav, Representations of two parameter quantum algebras and p,q-special functions, Journal of Mathematical Analysis and Applications, 335 (2007) 268–279.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood, Chichester, 1984.
Sarasvati Yadav and Geeta Rani, Certain Models of the Lie algebra K5 and their connection with Special Functions, kyungpook Mathematical journal, 58(2018), 615-625.