On the Kazhdan–Lusztig cells in type $E_8$

DOI10.1090/mcom/2963zbMath1335.20010arXiv1401.6804OpenAlexW1854074007MaRDI QIDQ5501160

Meinolf Geck, Abbie Halls

Publication date: 13 August 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6804

zbMATH Keywords

algorithmsfinite Coxeter groupsKazhdan-Lusztig cellsstar operationsLusztig \(a\)-function

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items

Invariant Bilinear Forms on W-Graph Representations and Linear Algebra Over Integral Domains, Conjugacy classes of involutions and Kazhdan–Lusztig cells, Kazhdan-Lusztig cells of \(\mathbf{a} \)-value 2 in \(\mathbf{a}(2)\)-finite Coxeter systems, The ABC of \(p\)-cells, Hecke algebras with unequal parameters and Vogan’s left cell invariants

Uses Software

• CHEVIE
• Coxeter

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kazhdan-Lusztig cells and the Frobenius-Schur indicator.
• The Hodge theory of Soergel bimodules.
• Representations of Hecke algebras at roots of unity.
• Cells in affine Weyl groups. II
• Ordering of the primitive spectrum of a semisimple Lie algebra
• On Iwahori-Hecke algebras with unequal parameters and Lusztig's isomorphism theorem.
• James' conjecture for Hecke algebras of exceptional type. I.
• Computational construction of irreducible \(W\)-graphs for types \(E_6\) and \(E_7\).
• The Kazhdan-Lusztig cells in certain affine Weyl groups
• On a theorem of Benson and Curtis
• Representations of Coxeter groups and Hecke algebras
• The left cells and their \(W\)-graphs of Weyl group of type \(F_ 4\)
• A generalized \(\tau\)-invariant for the primitive spectrum of a semisimple Lie algebra
• Left cells in the Weyl group of type \(E_8\)
• On the Kazhdan-Lusztig order on cells and families.
• The left cells of the Coxeter group of type \(H_ 4\)
• Rationality properties of unipotent representations.
• The state of the art in the computation of Kazhdan-Lusztig polynomials
• Left cells containing a fully commutative element.
• Positivity results for the Hecke algebras of noncrystallographic finite Coxeter groups.
• Conjugacy classes of involutions and Kazhdan–Lusztig cells
• On Domino Insertion and Kazhdan–Lusztig Cells in Type B n
• Characters of Reductive Groups over a Finite Field. (AM-107)
• KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS
• An Approach to the Connectedness of the Left Cells in Affine Weyl Groups
• Leading coefficients and cellular bases of Hecke algebras
• The representations and generic degrees of the Hecke algeba of type H4.
• Left cells in the weyl group of type₇
• ON THE INDUCTION OF KAZHDAN–LUSZTIG CELLS
• Involutions in Weyl groups
• Hecke Algebras with Unequal Parameters
• Left cells in weyl group of type E₆
• Hecke algebras and involutions in Weyl groups
• PyCox: computing with (finite) Coxeter groups and Iwahori–Hecke algebras
• On Kottwitz' conjecture for twisted involutions
• Relative Kazhdan–Lusztig cells