scholarly journals Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators

2000 ◽  
pp. 141-162 ◽  
Author(s):  
Yasushi Komori
Keyword(s):  
Theta Functions ◽  
Root Systems ◽  
Affine Root Systems

GENERALIZED mth ORDER JACOBI THETA FUNCTIONS AND THE MACDONALD IDENTITIES

2008 ◽  
Vol 04 (03) ◽  
pp. 461-474 ◽  
Author(s):  
PEE CHOON TOH
Keyword(s):  
Theta Function ◽  
Theta Functions ◽  
Root Systems ◽  
Jacobi Theta Functions ◽  
Multiple Variables ◽  
Affine Root Systems ◽  
Theta Function Identities

We describe an mth order generalization of Jacobi's theta functions and use these functions to construct classes of theta function identities in multiple variables. These identities are equivalent to the Macdonald identities for the seven infinite families of irreducible affine root systems. They are also equivalent to some elliptic determinant evaluations proven recently by Rosengren and Schlosser.

ROOT SYSTEMS ARISING FROM AUTOMORPHISMS

2012 ◽  
Vol 11 (03) ◽  
pp. 1250057 ◽  
Author(s):  
SAEID AZAM ◽  
MALIHE YOUSOSFZADEH
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Affine Lie Algebras ◽  
Combinatorial Approach ◽  
Reflection Algebras ◽  
Affine Root Systems ◽  
Outstanding Work ◽  
Affine Reflection

We study a combinatorial approach of producing new root systems from the old ones in the context of affine root systems and their new generalizations. The appearance of this approach in the literature goes back to the outstanding work of Kac in the realization of affine Kac–Moody Lie algebras. In recent years, this approach has been appeared in many other works, including the study of affinization of extended affine Lie algebras and invariant affine reflection algebras.

scholarly journals The Structure of Total Reflection Orders in Affine Root Systems

1998 ◽  
Vol 205 (1) ◽  
pp. 207-226 ◽  
Author(s):  
Paola Cellini ◽  
Paolo Papi
Keyword(s):  
Root Systems ◽  
Total Reflection ◽  
Affine Root Systems

scholarly journals Convex Orderings in Affine Root Systems

1995 ◽  
Vol 172 (3) ◽  
pp. 613-623 ◽  
Author(s):  
P. Papi
Keyword(s):  
Root Systems ◽  
Affine Root Systems
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