Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unity
نویسنده
چکیده
Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.
منابع مشابه
Hall-Littlewood functions at roots of unity
Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.
متن کاملRibbon Tableaux, Hall-littlewood Functions and Unipotent Varieties
We introduce a new family of symmetric functions, which are defined in terms of ribbon tableaux and generalize Hall-Littlewood functions. We present a series of conjectures, and prove them in two special cases.
متن کاملDistributed Computation of Ribbon Tableaux and Spin Polynominals
Recent works in algebraic combinatorics have brought up to date the importance of certain planar structures, called ribbon tableaux, which are generalizations of Young tableaux. This paper gives an algorithm to eeciently distribute, using PVM, the computation of the set of all ribbon tableaux of given shape and weight. It also provides a way to compute the spin polynomials associated to those s...
متن کاملA Cyclage Poset Structure for Littlewood-Richardson Tableaux
A graded poset structure is defined for the sets of LittlewoodRichardson (LR) tableaux that count the multiplicity of an irreducible gl(n)module in the tensor product of irreducible gl(n)-modules corresponding to rectangular partitions. This poset generalizes the cyclage poset on columnstrict tableaux defined by Lascoux and Schützenberger, and its grading function generalizes the charge statist...
متن کاملRibbon Operators and Hall-Littlewood Symmetric Functions
Abstract. Given a partition λ = (λ1, λ2, . . . λk), let λ rc = (λ2 − 1, λ3 − 1, . . . λk − 1). It is easily seen that the diagram λ/λ is connected and has no 2 × 2 subdiagrams which we shall refer to as a ribbon. To each ribbon R, we associate a symmetric function operator S. We may define the major index of a ribbon maj(R) to be the major index of any permutation that fits the ribbon. This pap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 115 شماره
صفحات -
تاریخ انتشار 2008