scholarly journals Some conjectures on the Schur expansion of Jack polynomials

2021 ◽  
Vol 12 (2) ◽  
pp. 215-233
Author(s):  
Per Alexandersson ◽  
James Haglund ◽  
George Wang
Keyword(s):  
Jack Polynomials

scholarly journals A Unified View of Determinantal Expansions for Jack Polynomials

10.37236/1547 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Leigh Roberts
Keyword(s):  
Differential Geometry ◽  
Symmetric Functions ◽  
Jack Polynomials ◽  
Elementary Symmetric Functions ◽  
Fundamental Symmetry ◽  
Unified View

Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions $m_\lambda$. We express these polynomials as determinants in elementary symmetric functions $e_\lambda$, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-Sutherland operator in physics or quasi Laplace Beltrami operators arising from differential geometry and statistics. Examples are given, and comments on the sparseness of the determinants so obtained conclude the paper.

scholarly journals Generalized clustering conditions of Jack polynomials at negative Jack parameterα

2008 ◽  
Vol 77 (18) ◽  
Author(s):  
B. Andrei Bernevig ◽  
F. D. M. Haldane
Keyword(s):  
Jack Polynomials

scholarly journals Highest weight Macdonald and Jack polynomials

2011 ◽  
Vol 44 (5) ◽  
pp. 055204 ◽  
Author(s):  
Th Jolicoeur ◽  
J G Luque
Keyword(s):  
Jack Polynomials ◽  
Highest Weight

scholarly journals Multilevel Dyson Brownian motions via Jack polynomials

2014 ◽  
Vol 163 (3-4) ◽  
pp. 413-463 ◽  
Author(s):  
Vadim Gorin ◽  
Mykhaylo Shkolnikov
Keyword(s):  
Jack Polynomials ◽  
Brownian Motions

scholarly journals On the evaluation formula for Jack polynomials with prescribed symmetry

2001 ◽  
Vol 34 (41) ◽  
pp. 8407-8424 ◽  
Author(s):  
P J Forrester ◽  
D S McAnally ◽  
Y Nikoyalevsky
Keyword(s):  
Jack Polynomials
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