Macdonald polynomials at $t=q^k$

Abstract

We investigate the homogeneous symmetric Macdonald polynomials $P_λ(\X;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_λ(\X;q,q^k)$ and $P_λ(\frac{1-q}{1-q^k}\X;q,q^k)$. As a consequence, we describe an operator whose eigenvalues characterize the polynomials $P_λ(\X;q,q^k)$.

19pp; Journal of Algebra (2009) In Press

References in corpus (2)

• Laughlin's wave functions, Coulomb gases and expansions of the discriminant
• Determinantal expressions for Macdonald polynomials

Cited by in corpus (1)

• Jack polynomial fractional quantum Hall states and their generalizations