scholarly journals Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

2020 ◽  
Author(s):  
Hjalmar Rosengren ◽  
◽  
Michael J. Schlosser ◽  
Keyword(s):  
Hypergeometric Series ◽  
Root Systems ◽  
Multidimensional Matrix ◽  
Multidimensional Matrix Inversions

scholarly journals Elliptic hypergeometric series on root systems

2004 ◽  
Vol 181 (2) ◽  
pp. 417-447 ◽  
Author(s):  
Hjalmar Rosengren
Keyword(s):  
Hypergeometric Series ◽  
Root Systems

scholarly journals From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Martin Hallnäs ◽  
Edwin Langmann ◽  
Masatoshi Noumi ◽  
Hjalmar Rosengren
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Root Systems ◽  
Higher Order ◽  
Explicit Description ◽  
Transformation Formula ◽  
Inverse Limits ◽  
First Order ◽  
Order Case ◽  
Multiple Basic Hypergeometric Series

AbstractKajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his formula, we deduce kernel identities for deformed Macdonald–Ruijsenaars (MR) and Noumi–Sano (NS) operators. The deformed MR operators were introduced by Sergeev and Veselov in the first order case and by Feigin and Silantyev in the higher order cases. As applications of our kernel identities, we prove that all of these operators pairwise commute and are simultaneously diagonalised by the super-Macdonald polynomials. We also provide an explicit description of the algebra generated by the deformed MR and/or NS operators by a Harish-Chandra type isomorphism and show that the deformed MR (NS) operators can be viewed as restrictions of inverse limits of ordinary MR (NS) operators.

A Technique for the Periodic Observation of Root Systems in Situ 1

1962 ◽  
Vol 54 (1) ◽  
pp. 56-56 ◽  
Author(s):  
T. J. Muzik ◽  
J. W. Whitworth
Keyword(s):  
Root Systems
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