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

Author(s):  
George Lusztig
Keyword(s):  
2005 ◽  
Vol 48 (2) ◽  
pp. 203-230 ◽  
Author(s):  
Takao Suzuki

1988 ◽  
Vol 205 (2-3) ◽  
pp. 281-284 ◽  
Author(s):  
D. Altschüler ◽  
J. Lacki ◽  
Ph. Zaugg

1994 ◽  
Vol 22 (6) ◽  
pp. 1955-1974 ◽  
Author(s):  
XIN-FA Zhang

2007 ◽  
Vol 18 (07) ◽  
pp. 839-868 ◽  
Author(s):  
HAJIME NAGOYA

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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