The Two-Sided Cells of the Affine Weyl Group of Type Ãn

1985 ◽  
pp. 275-283 ◽  
Author(s):  
George Lusztig
Keyword(s):  
Weyl Group ◽  
Affine Weyl Group

The affine Weyl group and modular invariant partition functions

1988 ◽  
Vol 205 (2-3) ◽  
pp. 281-284 ◽  
Author(s):  
D. Altschüler ◽  
J. Lacki ◽  
Ph. Zaugg
Keyword(s):  
Weyl Group ◽  
Partition Functions ◽  
Modular Invariant ◽  
Affine Weyl Group

QUANTUM PAINLEVÉ SYSTEMS OF TYPE $A_{n-1}^{(1)}$ WITH HIGHER DEGREE LAX OPERATORS

2007 ◽  
Vol 18 (07) ◽  
pp. 839-868 ◽  
Author(s):  
HAJIME NAGOYA
Keyword(s):  
Weyl Group ◽  
Heisenberg Algebra ◽  
Painlevé Equations ◽  
Differential Systems ◽  
Classical Systems ◽  
Painleve Equations ◽  
Type Formula ◽  
Affine Weyl Group ◽  
Lax Operator ◽  
Group Symmetries

Quantum Painlevé systems of type [Formula: see text] [13] are the quantizations of the second, fourth and fifth Painlevé equations and their generalizations [1, 15, 26]. These quantized systems have the Lax representations as in the classical systems. As a polynomial in an element of a Heisenberg algebra of [Formula: see text], the degrees of those Lax operators are 2 or 3. In this paper, we shall deal with the Lax operator whose degree is greater than or equal to 2. Using this Lax operator, we systematically construct the differential systems with the affine Weyl group symmetries of type [Formula: see text] and the commuting Hamiltonians.

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