Sumários

11 Novembro 2025, 10:00 • Marko Stosic

Skew-Schur functions (continuation).

Schur polynomials via semi-standard Young tableaux.

Kostka numbers.

Contents and hook-lengths of a Young diagram.

4 Novembro 2025, 10:00 • Marko Stosic

Skew-Schur functions.

Schur and skew-Schur polynomials from semi-standard Young tableaux

and skew-Young tableaux.

28 Outubro 2025, 10:00 • Marko Stosic

Hall inner product on the ring of symmetric functions.

Schur functions as an orthonormal basis with respect to the Hall inner product.

21 Outubro 2025, 10:00 • Marko Stosic

Schur functions as elements of the ring of symmetric functions.

Jacobi-Trudy formulas: expressing Schur polynomials as a function (determinant) of complete symmetric functions,

and of elementary symmetric functions.

Involution of a Schur function: equals to the Schur function of the dual partition.

14 Outubro 2025, 10:00 • Marko Stosic

(Monomial) basis of alternating (antisymmetric) polynomials.

Definition of Schur polynomials (as quotient of basis alternating polynomial and Vandermonde determinant).

Schur polynomials form Z-basis of the ring of symmetric polynomials.

First explicit computations of Schur polynomials.

Semi-standard Young tableaux, and the corresponding monomials.

Schur polynomial as the sum of monomials corresponding to all semi-standard Young tableaux corresponding to the Young diagram of a partition.