# Positive Jantzen sum formulas for cyclotomic Hecke algebras

@article{Mathas2022PositiveJS,
title={Positive Jantzen sum formulas for cyclotomic Hecke algebras},
author={Andrew Mathas},
journal={Mathematische Zeitschrift},
year={2022},
volume={301},
pages={2617 - 2658}
}
• A. Mathas
• Published 29 June 2021
• Mathematics
• Mathematische Zeitschrift
This paper proves a “positive” Jantzen sum formula for the Specht modules of the cyclotomic Hecke algebras of type A and uses it to obtain new bounds on decomposition numbers. Quite remarkably, our results are proved entirely inside the cyclotomic Hecke algebras. Our positive sum formula shows that, in the Grothendieck group, the Jantzen sum formula can be written as an explicit non-negative linear combination of modules [Ef,eν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage…
1 Citations

### Graded sum formula for $\tilde{A}_1$-Soergel calculus and the nil-blob algebra

• Mathematics
• 2022
We study the representation theory of the Soergel calculus algebra A w := End D ( W,S ) ( w ) over C in type ˜ A 1 . We generalize the recent isomorphism between the nil-blob algebra NB n and A w to

## References

SHOWING 1-10 OF 50 REFERENCES

### ON BASES OF SOME SIMPLE MODULES OF SYMMETRIC GROUPS AND HECKE ALGEBRAS

• Mathematics
• 2016
We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules Dλ, labelled by e-restricted partitions λ of n, for a cyclotomic

### Cyclotomic quiver Hecke algebras of type A

This chapter is based on a series of lectures that I gave at the National University of Singapore in April 2013. The notes survey the representation theory of the cyclotomic Hecke algebras of type A

### Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras

• Mathematics
• 2012
In this paper, we prove Khovanov-Lauda’s cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let $U_{q}(\mathfrak{g})$ be the quantum group associated with a

### Seminormal forms and cyclotomic quiver Hecke algebras of type A

• Mathematics
• 2013
This paper shows that the cyclotomic quiver Hecke algebras of type A, and the gradings on these algebras, are intimately related to the classical seminormal forms. We start by classifying all

### Representations of Coxeter groups and Hecke algebras

• Mathematics
• 1979
here l(w) is the length of w. In the case where Wis a Weyl group and q is specialized to a fixed prime power, | ~ can be interpreted as the algebra of intertwining operators of the space of functions

### Quantum Groups

• Mathematics
• 1993
This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions

### Hecke algebras at roots of unity and crystal bases of quantum affine algebras

• Mathematics
• 1996
AbstractWe present a fast algorithm for computing the global crystal basis of the basic $$U_q (\widehat{\mathfrak{s}\mathfrak{l}}_n )$$ -module. This algorithm is based on combinatorial techniques

### Cellular algebras

• Mathematics
• 1996
AbstractA class of associative algebras (“cellular”) is defined by means of multiplicative properties of a basis. They are shown to have cell representations whose structure depends on certain