$gl_{n+1}$ algebra of Matrix Differential Operators and Matrix Quasi-exactly-solvable Problems
Abstract
The generators of the algebra $gl_{n+1}$ in a form of differential operators of the first order acting on ${\bf R}^n$ with matrix coefficients are explicitly written. The algebraic Hamiltonians for a matrix generalization of $3-$body Calogero and Sutherland models are presented.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2013
- DOI:
- 10.48550/arXiv.1306.1377
- arXiv:
- arXiv:1306.1377
- Bibcode:
- 2013arXiv1306.1377S
- Keywords:
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- Mathematical Physics;
- Mathematics - Representation Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 22 pages, 2 figures, Dedicated to Miloslav Havlicek on the occasion of his 75th birthday