99 research outputs found
Pieri's formula for generalized Schur polynomials
No full textYoung's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutating relation of generalized Schur operators implies Pieri's formula to generalized Schur polynomials
Pieri's formula for generalized Schur polynomials(The world of Combinatorial Representation Theory)
No full textOn an edge-signed generalization of chordal graphs and free multiplicities on braid arrangements (Representation Theory and Combinatorics)
No full textOn a bijective proof of a factorization formula for Macdonald polynomials at roots of unity (Expansion of Combinatorial Representation Theory)
No full textTabloids and weighted sums of characters of certain modules of the symmetric groups
No full textWe consider certain modules of the symmetric groups whose basis elements are called tabloids. Some of these modules are isomorphic to subspaces of the cohomology rings of subvarieties of flag varieties as modules of the symmetric groups. We give a combinatorial description for some weighted sums of their characters, i.e., we introduce combinatorial objects called (½; l)-tableaux and rewrite weighted sums of characters as the numbers of these combinatorial objects. We also consider the meaning of these combinatorial objects, i.e., we construct a correspondence between (½; l)-tableaux and tabloids whose images are eigenvectors of the action of an element of cycle type ½ in quotient modules
On moments of the noncentral Wishart distributions and weighted generating functions of matchings (Combinatorial Representation Theory and its Applications)
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