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Goodman, Frederick M.; Wenzl, Hans

doi:10.1155/s1073792899000136

Cited by 17 publications

(3 citation statements)

References 12 publications

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“…s rm as a product of elementary transpositions with m as small as possible. Define 12) noting that (in general) ψ w depends on the choice of a reduced expression for w. By definition, the length of w is (w) := m.…”

Section: )mentioning

confidence: 99%

“…The notation in [21,Theorem 3.1] is different from that of Theorem 4.8 or Lemma 4.7, but it is not difficult to see that the results are equivalent. Alternatively, a direct proof of Theorem 4.8 can be easily obtained via the fact that the decomposition numbers [S λ F : D µ F ] q are certain parabolic Kazhdan-Lusztig polynomials, see [26] or [12,Theorem 5.3], together with Soergel's algorithm [25] for computing those polynomials.…”

Section: Decomposition Numbers Setmentioning

confidence: 99%

See 1 more Smart Citation

On Bases of Some Simple Modules of Symmetric Groups and Hecke Algebras

Boeck¹,

Evseev²,

Lyle³

et al. 2017

Transformation Groups

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We record with deep sadness the passing of Anton Evseev on 21st February 2017 Abstract. We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules D λ , labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra R Λ0 n over a field of characteristic p 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde,p(λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of D λ . In particular, we prove that the q-character of D λ can be described in terms of DStde,p(λ).We show that a certain natural approach to constructing a basis of an arbitrary D λ does not work in general, giving a counterexample to a conjecture of Mathas.

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Section: )mentioning

confidence: 99%

Section: Decomposition Numbers Setmentioning

confidence: 99%

On Bases of Some Simple Modules of Symmetric Groups and Hecke Algebras

Boeck¹,

Evseev²,

Lyle³

et al. 2017

Transformation Groups

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“…Corollary 3.5.27 determines the graded decomposition numbers of the cyclotomic Hecke algebras in characteristic zero. There are several different algorithms for computing the graded decomposition numbers in characteristic zero [40,46,55,82,89,131]. To determine the graded decomposition numbers in positive characteristic it is enough to compute the adjustment matrices of Theorem 3.7.6.…”

Section: The Sgn Map Induces An Equivalence Repmentioning

confidence: 99%

CYCLOTOMIC QUIVER HECKE ALGEBRAS OF TYPE A

Mathas

2015

Modular Representation Theory of Finite and p-Adic Groups

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Contents n 1.6. Semisimple cyclotomic Hecke algebras of type A 1.7. Gram determinants and the Jantzen sum formula 1.8. The blocks of H F n 2. Cyclotomic quiver Hecke algebras of type A 2.1. Graded algebras 2.2. Cyclotomic quiver Hecke algebras 2.3. Nilpotence and small representations 2.4. Semisimple KLR algebras 2.5. The nil-Hecke algebra 3. Isomorphisms, Specht modules and categorification 3.1. The Graded Isomorphism Theorem 3.2. Graded Specht modules 3.3. Blocks and dual Specht modules 3.4. Induction and restriction 3.5. Grading Ariki's Categorification Theorem 3.6. Homogeneous Garnir relations 3.7. Graded adjustment matrices 4. Seminormal bases and the KLR grading 4.1. Gram determinants and graded dimensions 4.2. A deformation of the KLR grading 4.3. A distinguished homogeneous basis 4.4. A simple conjecture References

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Curing of Composites and Adhesives

Makuuchi¹,

Cheng²

2011

Radiation Processing of Polymer Materials and Its Industrial Applications

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Cited by 17 publications

References 12 publications

On Bases of Some Simple Modules of Symmetric Groups and Hecke Algebras

On Bases of Some Simple Modules of Symmetric Groups and Hecke Algebras

CYCLOTOMIC QUIVER HECKE ALGEBRAS OF TYPE A

Curing of Composites and Adhesives

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