10 citations · 28 across the 14 of their papers we have counts for
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Non symmetric Cauchy kernels for the classical Groups
Amy M. Fu, Alain Lascoux
We give non-symmetric versions of the Cauchy kernel and Littlewood's kernels, corresponding to the types , , and , of the classical groups. We show that these…
Pfaffians and Representations of the Symmetric Group
Alain Lascoux
Pfaffians of matrices with entries z[i,j]/(x\_i+x\_j), or determinants of matrices with entries z[i,j]/(x\_i-x\_j), where the antisymmetrical indeterminates z[i,j] satisfy the Plüc…
The 6 Vertex Model and Schubert Polynomials
Alain Lascoux
We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The result…
Non-Symmetric Hall-Littlewood Polynomials
Francois Descouens, Alain Lascoux
Using the action of the Yang-Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall-Littlewood polynomials are a subfamily…
The differential equation satisfied by a plane curve of degree n
Alain Lascoux
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order by computing sufficiently many derivatives, one obtains a differential equation. This i…
The Hecke algebra and structure constants of the ring of symmetric polynomials
Alain Lascoux
We give half a dozen bases of the Hecke algebra of the symmetric group, and relate them to the basis of Geck-Rouquier, and to the basis of Jones, using matrices of change of bases…