Some Plethystic Identites and Kostka-foulkes Polynomials
نویسنده
چکیده
plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → ΛQ(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image∇(En,k(X)) of En,k(X) is equal to the following combinatorial summation
منابع مشابه
Hall-littlewood Vertex Operators and Generalized Kostka Polynomials Mark Shimozono and Mike Zabrocki
Kostka-Folkes polynomials may be considered as coefficients of the formal power series representing the character of certain graded GL(n)-modules. These GL(n)-modules are defined by twisting the coordinate ring of the nullcone by a suitable line bundle [1] and the definition may be generalized by twisting the coordinate ring of any nilpotent conjugacy closure in gl(n) by a suitable vector bundl...
متن کاملSome Plethystic Identities And Kostka-Foulkes Polynomials
plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → Λ n Q(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image ∇(En,k(X))...
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The Kostka-Foulkes polynomials K λ,μ(q) related to a root system φ can be defined as alternated sums running over the Weyl group associated to φ. By restricting these sums over the elements of the symmetric group when φ is of type Bn, Cn orDn, we obtain again a class K̃ φ λ,μ(q) of Kostka-Foulkes polynomials. When φ is of type Cn or Dn there exists a duality beetween these polynomials and some n...
متن کامل1 7 Ja n 20 05 Branching rules , Kostka - Foulkes polynomials and q - multiplicities in tensor product for the root systems
The Kostka-Foulkes polynomials K λ,μ(q) related to a root system φ can be defined as alternated sums running over the Weyl group associated to φ. By restricting these sums over the elements of the symmetric group when φ is of type Bn, Cn orDn, we obtain again a class K̃ φ λ,μ(q) of Kostka-Foulkes polynomials. When φ is of type Cn or Dn there exists a duality beetween these polynomials and some n...
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