On the seminormal bases and dual seminormal bases of the cyclotomic Hecke algebras of type G(ℓ,1,n)

@article{Hu2022OnTS,
  title={On the seminormal bases and dual seminormal bases of the cyclotomic Hecke algebras of type G(ℓ,1,n)},
  author={Jun Hu and Shixuan Wang},
  journal={Journal of Algebra},
  year={2022}
}
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2 Citations
Methods Citations
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2 Citations

Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras

Proof of the Center Conjectures for the cyclotomic Hecke and KLR algebras of type $A$

. The center conjectures for the cyclotomic Hecke algebra H Λ n,K of type G ( r, 1 ,n ) assert that (1) the dimension of the center Z ( H Λ n,K ) is independent of the characteristic of the ground…

References

SHOWING 1-10 OF 28 REFERENCES

Representation Theory of a Hecke Algebra of G(r, p, n)

Abstract In our previous paper [1], we introduced a notion of a Hecke algebra for a series of complex reflection groups ( Z /r Z ) ≀ K n, which is the group of n by n permutation matrices with…

Seminormal forms and cyclotomic quiver Hecke algebras of type A

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…

On the decomposition numbers of the Hecke algebra of $G(m, 1, n)$

This algebra is known to be A -free. If we specialize it to v i = v,, q= q, where vi e C, qe Cx, this algebra is denoted by i(c. W e note here that the study of this algebra over a ring of integers…

Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras

In this paper we prove theorems that describe how the representation theory of the affine Hecke algebra of type A and of related algebras such as the group algebra of the symmetric group are…

On the representation theory of the symmetric groups and associated Hecke algebras

Cellular algebras

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…

Schur–Weyl duality for higher levels

Abstract.We extend Schur–Weyl duality to an arbitrary level l ≥ 1, level one recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is…

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification…

Cyclotomic Nazarov-Wenzl Algebras

Abstract Nazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain “cyclotomic…

Fayers’ conjecture and the socles of cyclotomic Weyl modules

  • Jun HuA. Mathas
  • Mathematics
    Transactions of the American Mathematical Society
  • 2018
Gordon James proved that the socle of a Weyl module of a classical Schur algebra is a sum of simple modules labelled by p p -restricted partitions. We prove an analogue of this result in the…