scholarly journals Lusztig's q-analogue of weight multiplicity and one-dimensional sums for affine root systems

2007 ◽  
Vol 208 (1) ◽  
pp. 438-466 ◽  
Author(s):  
Cédric Lecouvey ◽  
Mark Shimozono
Keyword(s):  
Root Systems ◽  
One Dimensional ◽  
Weight Multiplicity ◽  
Affine Root Systems

scholarly journals Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities

2020 ◽  
pp. 2050024 ◽  
Author(s):  
Andrei Velicu
Keyword(s):  
Hardy Inequality ◽  
Root Systems ◽  
Dunkl Operators ◽  
Hardy Inequalities ◽  
One Dimensional ◽  
Hardy Type Inequalities ◽  
Rellich Inequality ◽  
Nirenberg Inequality ◽  
Special Case ◽  
The Hardy Inequality

In this paper, we study various forms of the Hardy inequality for Dunkl operators, including the classical inequality, [Formula: see text] inequalities, an improved Hardy inequality, as well as the Rellich inequality and a special case of the Caffarelli–Kohn–Nirenberg inequality. As a consequence, one-dimensional many-particle Hardy inequalities for generalized root systems are proved, which in the particular case of root systems [Formula: see text] improve some well-known results.

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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