General runner removal and the Mullineux map Matthew Fayers

نویسنده

  • Matthew Fayers
چکیده

We prove a new ‘runner removal theorem’ for q-decomposition numbers of the level 1 Fock space of typeA (1) e−1 , generalising earlier theorems of James–Mathas and the author. By combining this with another theorem relating to the Mullineux map, we show that the problem of finding all q-decomposition numbers indexed by partitions of a given weight is a finite computation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Regularisation and the Mullineux Map

We classify the pairs of conjugate partitions whose regularisations are images of each other under the Mullineux map. This classification proves a conjecture of Lyle, answering a question of Bessenrodt, Olsson and Xu.

متن کامل

Another runner removal theorem for v-decomposition numbers of Iwahori–Hecke algebras and q-Schur algebras

Let F denote the Fock space representation of the quantum groupUv(ŝle). The ‘v-decomposition numbers’ are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions, and the evaluations at v = 1 of these polynomials give the decomposition numbers for Iwahori–Hecke algebras and q-Schur algebras over C. James and Mathas have proved a theorem ...

متن کامل

On Residue Symbols and the Mullineux Conjecture

This paper is concerned with properties of the Mullineux map, which plays a rôle in p-modular representation theory of symmetric groups. We introduce the residue symbol for a p-regular partitions, a variation of the Mullineux symbol, which makes the detection and removal of good nodes (as introduced by Kleshchev) in the partition easy to describe. Applications of this idea include a short proof...

متن کامل

Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules

We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke ...

متن کامل

Monomial Crystals and Partition Crystals

Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal B(Λ0) for b sln, where the vertices are indexed by certain partitions. He showed that special cases of this construction agree with the Misra-Miwa realization and with Berg’s ladder crystal. Here we show that another special case is naturally isomorphic to a realization using Nakajima’s monomial c...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009