arXiv subjects

Luc Lapointe

Publications and source records attributed to Luc Lapointe.

39 records · Page 3Linked to original sources

arXiv1996

A short proof of the integrality of the Macdonald (q,t)-Kostka coefficients

The Macdonald polynomials can be obtained by acting on the constant 1 with creation operators. Three different expressions for these operators are derived, one from the other, in a rather succint way. When the last of these expressions is used, the formalism is seen to imply straightforwardly the integrality of the (q,t)-Kostka coefficients, that is of the expansion coefficients for the Macdonald functions in terms of Schur functions.

q-alg↗

arXiv1995

A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture

A formula of Rodrigues-type for the Jack polynomials is presented. It is seen to imply a weak form of a conjecture of Macdonald and Stanley.

q-alg↗

arXiv1995

Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.

q-alg↗