Papers › Bialternant formula for Schur polynomials with repeating variables
Bialternant formula for Schur polynomials with repeating variables
Luis Angel González-Serrano, Egor A. Maximenko
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We consider polynomials of the form s_λ(y₁^([ϰ₁]),…,yₙ^([ϰₙ])), where λ is an integer partition, s_λ is the Schur polynomial associated to λ, and yⱼ^([ϰⱼ]) denotes yⱼ repeated ϰⱼ times. We represent s_λ(y₁^([ϰ₁]),…,yₙ^([ϰₙ])) as a quotient whose the denominator is the determinant of the confluent Vandermonde matrix, and the numerator is the determinant of some generalized confluent Vandermonde matrix. We give three algebraic proofs of this formula.
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