Cells in affine Weyl groups. II
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Publication:579413
DOI10.1016/0021-8693(87)90154-2zbMath0625.20032OpenAlexW1980273061MaRDI QIDQ579413
Publication date: 1987
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-8693(87)90154-2
affine Weyl groupsCoxeter groupsinvolutionsenveloping algebraGelfand-Kirillov dimensionHecke algebraleft cell
Representation theory for linear algebraic groups (20G05) Universal enveloping (super)algebras (17B35) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Homological dimension in associative algebras (16E10) Associated Lie structures for groups (20F40)
Related Items (98)
Left cells in affine Weyl groups ⋮ 2-representations of small quotients of Soergel bimodules in infinite types ⋮ Left cells containing a fully commutative element. ⋮ The Steinberg variety and representations of reductive groups. ⋮ Perverse sheaves on affine flags and nilpotent cone of the Langlands dual group ⋮ Intersecting principal Bruhat ideals and grades of simple modules ⋮ Parabolic projective functors in type \(A\) ⋮ On generalized cells in affine Weyl groups ⋮ Some translations in the second lowest two-sided cell of an affine Weyl group ⋮ Cell decomposition in the affine weyl group wA([Btilde4)] ⋮ Canonical left cells in affine Weyl groups ⋮ Constructing cell data for diagram algebras. ⋮ The relation \(\mathop{\leqslant}\limits_{\mathrm{LR}}\) on some elements of the affine Weyl group \(\tilde{C}_n\) ⋮ Some left cells in the affine Weyl group Ẽ6 ⋮ Left cells witha-value 4 in the affine weyl group of type[btilden] ⋮ Minimal length elements of extended affine Weyl groups ⋮ On embedding certain Kazhdan-Lusztig cells of \(S_n\) into cells of \(S_{n+1}\) ⋮ Some homological properties of category \(\mathcal{O}\). IV ⋮ Isomorphisms between affine Hecke algebras of type \(\widetilde{A_2}\). ⋮ The leading coefficients for an affine Weyl group of type \(\widetilde{G_2}\): the lowest two-sided cell case ⋮ Left cells in the affine Weyl group of type \(\widetilde F_4\) ⋮ On the computation of Kazhdan-Lusztig polynomials and representations of Hecke algebras ⋮ Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra. II. ⋮ The lowest two-sided cell of a Coxeter group with complete graph ⋮ Lengths of involutions in finite Coxeter groups ⋮ Affine cellularity of affine Yokonuma-Hecke algebras ⋮ Kazhdan-Lusztig cells and the Frobenius-Schur indicator. ⋮ On the structure of the affine asymptotic Hecke algebras ⋮ The distinguished involutions with \(a\)-value \(n^2-3n+3\) in the Weyl group of type \(D_n\). ⋮ Boolean intersection ideals of permutations in the Bruhat order ⋮ Kazhdan-Lusztig cells of \(\mathbf{a} \)-value 2 in \(\mathbf{a}(2)\)-finite Coxeter systems ⋮ Left cells in weyl group of type E6 ⋮ The based rings of two-sided cells in an affine Weyl group of type \(\tilde{B}_3\). I ⋮ Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type \(\widetilde A_n\). ⋮ The second lowest two-sided cell in the affine Weyl group \(\widetilde{B}_n\) ⋮ Characters for unipotent representations ⋮ Homological invariants in category $\mathcal {O}$ for the general linear superalgebra ⋮ The lowest two-sided cell for an affine weyl group ⋮ The decomposition into cells of the affine weyl group of type [Btilde3] ⋮ Hochschild homology of affine Hecke algebras. ⋮ Lusztig's \(a\)-function for Coxeter groups of rank 3. ⋮ Cells in Coxeter groups. I. ⋮ \(W\)-graph versions of tensoring with the \(\mathcal S_n\) defining representation. ⋮ Left Cells witha-Value 4 in the Affine Weyl Groups (i = 6, 7, 8) ⋮ The second lowest two-sided cell in an affine Weyl group. ⋮ Conjectures P1--P15 for Coxeter groups with complete graph ⋮ Support varieties for quantum groups ⋮ Affine cellular algebras. ⋮ Motives with exceptional Galois groups and the inverse Galois problem ⋮ On certain distinguished involutions in the Weyl group of type \(D_n\). ⋮ The generalized Robinson-Schensted algorithm on the affine Weyl group of type \(A_{n-1}\) ⋮ Joint relations on elements of the symmetric group. ⋮ Simple transitive 2-representations of small quotients of Soergel bimodules ⋮ On Lusztig’s asymptotic Hecke algebra for 𝑆𝐿₂ ⋮ Some homological properties of category \(\mathcal{O}\). VI ⋮ The cells in the weighted Coxeter group \((\widetilde C_n,\widetilde\ell_m)\). ⋮ Classification of Coxeter groups with finitely many elements of \(\mathfrak{a}\)-value 2 ⋮ The ABC of \(p\)-cells ⋮ On the determination of Kazhdan-Lusztig cells for affine Weyl groups with unequal parameters. ⋮ The based ring of the lowest two-sided cell of an affine Weyl group. III ⋮ The based ring of the lowest generalized two-sided cell of an extended affine Weyl group ⋮ THE LEFT CELLS OF THE AFFINE WEYL GROUP OF TYPE [Dtilde5] ⋮ Left-connectedness of some left cells in certain Coxeter groups of simply-laced type. ⋮ Unnamed Item ⋮ PyCox: computing with (finite) Coxeter groups and Iwahori–Hecke algebras ⋮ Left V-cells for hyperbolic coxeter groups ⋮ Fully commutative elements in the Weyl and affine Weyl groups. ⋮ Note on the minimal permutations ⋮ A counter-example to a conjecture of Lusztig. ⋮ Computing Kazhdan-Lusztig cells for unequal parameters. ⋮ The leading coefficient of certain Kazhdan-Lusztig polynomials of the permutation group \({\mathfrak S}_n\). ⋮ Kazhdan-Lusztig coefficients for an affine Weyl group of type \(\widetilde B_2\). ⋮ On the injectivity of the Braid group in the Hecke algebra ⋮ Fully commutative Kazhdan-Lusztig cells ⋮ Properties of four partial orders on standard Young tableaux ⋮ The distinguished involutions of the weyl group of typeE6 ⋮ Kazhdan-Lusztig basis, Wedderburn decomposition, and Lusztig's homomorphism for Iwahori-Hecke algebras. ⋮ Bigrassmannian permutations and Verma modules ⋮ On the subregular \(J\)-rings of Coxeter systems ⋮ Some homological properties of category \(\mathcal{O}\). III ⋮ Epipelagic representations and rigid local systems ⋮ Left cells in the affine Weyl group of type \(\widetilde C_4\) ⋮ $C^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations ⋮ Comparison of \(a\)-functions ⋮ The joint relations and the set \({\mathcal D}_ 1\) in certain crystallographic groups ⋮ On Certain Distinguished Involutions in the Weyl Group of Type Bn ⋮ Unnamed Item ⋮ Unnamed Item ⋮ KOSTANT'S PROBLEM AND PARABOLIC SUBGROUPS ⋮ On the Humphreys conjecture on support varieties of tilting modules ⋮ Subregular \(J\)-rings of Coxeter systems via quiver path algebras ⋮ On the Kazhdan–Lusztig cells in type $E_8$ ⋮ Left cells in the weyl group of type7 ⋮ Left cells in the Weyl group of type \(E_8\) ⋮ Tabular algebras and their asymptotic versions. ⋮ Minimal and maximal elements in two-sided cells of \(S_n\) and Robinson-Schensted correspondence ⋮ Coxeter elements and Kazhdan-Lusztig cells ⋮ Cells in the affine Weyl group of type \(\tilde D_ 4\)
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