Symmetric and non-symmetric quantum Capelli polynomials
In "Difference operators and symmetric functions
defined by their zeros" (joint with Siddhartha Sahi) we introduced
a new family of symmetric polynomials which are related to Capelli
identities. The purpose of this paper is twofold: I quantize the
construction and obtain symmetric polynomials depending on two
parameters q and t. More importantly, I introduce an analogous family
of non-symmetric polynomials. It is shown that these form an
eigenbasis for certain q-difference equations. As a corollary, I
obtain that the top homogeneous part is a symmetric/non-symmetric
Macdonald polynomial. Finally the results of Integrality of two variable Kostka functions are
generalized by obtaining integrality results for the quantum Capelli
polynomials.
Appeared in: Commentarii Mathematici Helvetici
72 (1997) 84-100
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Last updated: October 26, 2000