The h-expansion of Macdonald operators and their expression by Dunkl operators

Details The h-expansion of Macdonald operators and their expression by Dunkl operators The h-expansion of Macdonald operators and their expression by Dunkl operators

2012-04-11

arxiv.org/abs/1204.2412v2

Mathematics

Quantum Algebra

32 pages

Scientific paper

Macdonald operators are well known as the 'commutative family' acting on the symmetric functions over Q(q,t). If we suppose that q=exp(h) and t=exp(beta h) and observe the Taylor expansion around h=0, we can see the second-degree Dunkl operator appear especially as the coefficient of h^2. These Dunkl operators also consist of commutative family. Then, as to the coefficient of h^3, it is natural to expect that third-degree Dunkl operator appears. The object of this paper is to calculate the coefficients of h^3 in the h-expansion of Macdonald operators explicitly, to introduce the method of calculation, and to prove that they can be expressed as the polynomials of Dunkl operators.

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