Ribbon tableaux, ribbon rigged configurations and Hall–Littlewood functions at roots of unity
نویسندگان
چکیده
منابع مشابه
Ribbon tableaux, ribbon rigged configurations and 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 Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.
متن کاملCombinatorics of Ribbon Tableaux
This thesis begins with the study of a class of symmetric functions {x} which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators on the space of partitions. I develop the theory of ribbon functions using these operators in an ...
متن کاملHall-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.
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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 کاملPieri and Cauchy Formulae for Ribbon Tableaux
In [LLT] Lascoux, Leclerc and Thibon introduced symmetric functions Gλ which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these functions in analogy with Schur functions. In particular we will describe: • a Pieri and dual-Pieri formula for ribbon functions, • a ribbon Murnaghan-Nakayama formula, • ribbon Cauchy and dual Cauchy identities, • and...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2008
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2007.06.005