1 1 A ug 1 99 8 Determinantal expressions for Macdonald polynomials
نویسنده
چکیده
We show that the action of classical operators associated to the Mac-donald polynomials on the basis of Schur functions, S λ [X(t − 1)/(q − 1)], can be reduced to addition in λ−rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, S λ [X], and the monomial basis, m λ [X].
منابع مشابه
. C O ] 3 1 M ar 1 99 9 Formulas for special cases of Macdonald polynomials Mike
An explicit expansion for the Macdonald polynomials of the form H (32 a 1 b) [X; q, t] and H (41 k) [X; q, t] in terms of Hall-Littlewood symmetric functions is presented. The expansion gives a proof of a symmetric function operator that adds a row of size 3 to Macdonald polynomials of the form H (2 a 1 b) [X; q, t] and another operator that adds a row of size 4 to Macdonald polynomials of only...
متن کاملar X iv : m at h / 98 04 02 7 v 1 [ m at h . C A ] 6 A pr 1 99 8 BIORTHOGONAL ENSEMBLES
Abstract. One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one–parametric deformation of these ensembles, which is defined in terms of the biorthogonal polynomials of Jacobi, Laguerre and Hermite type. Our main result is a series of explicit expressio...
متن کاملSome Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, and present several new recurrence relations for the Bernoulli numbers and polynomials.
متن کاملA ug 1 99 6 8 LECTURES ON QUANTUM GROUPS AND q - SPECIAL FUNCTIONS
The lecture notes contains an introduction to quantum groups, q-special functions and their interplay. After generalities on Hopf algebras, orthogonal polynomials and basic hypergeometric series we work out the relation between the quantum SU(2) group and the Askey-Wilson polynomials out in detail as the main example. As an application we derive an addition formula for a two-parameter subfamily...
متن کاملar X iv : q - a lg / 9 60 80 20 v 1 2 3 A ug 1 99 6 SHIFTED JACK POLYNOMIALS , BINOMIAL FORMULA , AND APPLICATIONS
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998