Lax operator for Macdonald symmetric functions

TY - JOUR

T1 - Lax operator for Macdonald symmetric functions

AU - Nazarov, Maxim

AU - Sklyanin, Evgeny

N1 - © Springer Science+Business Media Dordrecht 2015. This is an author produced version of a paper published in Letters in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the variables and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function.

AB - Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the variables and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function.

U2 - 10.1007/s11005-015-0770-1

DO - 10.1007/s11005-015-0770-1

M3 - Article

SN - 1573-0530

VL - 105

SP - 901

EP - 916

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 7

ER -