Involution words: counting problems and connections to Schubert calculus for symmetric orbit closures

DOI10.1016/j.jcta.2018.06.012zbMath1394.05139arXiv1508.01823OpenAlexW2252710755WikidataQ129501022 ScholiaQ129501022MaRDI QIDQ1671782

Eric Marberg, Brendan Pawlowski, Zachary Hamaker

Publication date: 7 September 2018

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.01823

zbMATH Keywords

permutationsCoxeter groupsinvolutionsBruhat orderSchubert polynomialsreduced wordsspherical varietiesStanley symmetric functions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (25)

On pattern avoidance in matchings and involutions ⋮ On some actions of the 0-Hecke monoids of affine symmetric groups ⋮ Actions of the 0-Hecke monoids of affine symmetric groups ⋮ $DIII$ clan combinatorics for the orthogonal Grassmannian ⋮ Involution words. II: Braid relations and atomic structures ⋮ Atoms for signed permutations ⋮ Enriched set-valued \(P\)-partitions and shifted stable Grothendieck polynomials ⋮ Bijecting hidden symmetries for skew staircase shapes ⋮ Queer supercrystal structure for increasing factorizations of fixed-point-free involution words ⋮ On some properties of symplectic Grothendieck polynomials ⋮ Shifted insertion algorithms for primed words ⋮ Quasiparabolic sets and Stanley symmetric functions for affine fixed-point-free involutions ⋮ Involution Schubert-Coxeter combinatorics ⋮ Transition formulas for involution Schubert polynomials ⋮ On involutions in Weyl groups ⋮ Principal specializations of Schubert polynomials in classical types ⋮ Affine transitions for involution Stanley symmetric functions ⋮ Bialgebras for Stanley symmetric functions ⋮ Involution pipe dreams ⋮ Stanley symmetric functions for signed involutions ⋮ Stanley symmetric functions for signed involutions ⋮ A symplectic refinement of shifted Hecke insertion ⋮ Involution pipe dreams ⋮ Universal graph Schubert varieties ⋮ \(K\)-theory formulas for orthogonal and symplectic orbit closures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Positivity conjectures for Kazhdan-Lusztig theory on twisted involutions: the finite case.
• Relating Edelman-Greene insertion to the Little map
• Polynomials for \(\mathrm{GL}_p\times \mathrm{GL}_q\) orbit closures in the flag variety
• Bruhat order on the involutions of classical Weyl groups.
• Chains in weak order posets associated to involutions
• The Bruhat order on symmetric varieties
• Twisted identities in Coxeter groups.
• Schubert polynomials and the Littlewood-Richardson rule
• On the number of reduced decompositions of elements of Coxeter groups
• Shifted tableaux and the projective representations of symmetric groups
• Flags, Schubert polynomials, degeneracy loci, and determinantal formulas
• Dual equivalence with applications, including a conjecture of Proctor
• Some combinatorial properties of Schubert polynomials
• Complements to `The Bruhat order on symmetric varieties'
• Schubert polynomials and the nilCoxeter algebra
• The behavior at infinity of the Bruhat decomposition
• Staircase skew Schur functions are Schur \(P\)-positive
• The Bruhat order on the involutions of the symmetric group
• Transition formulas for involution Schubert polynomials
• On the fully commutative elements of Coxeter groups
• Combinatorics of Fulton's essential set
• Balanced tableaux
• Combinatorial aspects of the Lascoux-Schützenberger tree
• Deformations of permutation representations of Coxeter groups.
• \(K\)-orbit closures on \(G/B\) as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form
• Involution words. II: Braid relations and atomic structures
• Coincidences among skew Schur functions
• Fixed points of involutive automorphisms of the Bruhat order
• Weak order on complete quadrics
• Positivity conjectures for Kazhdan-Lusztig theory on twisted involutions: the universal case
• Affine Stanley symmetric functions
• The combinatorics of twisted involutions in Coxeter groups
• RC-Graphs and Schubert Polynomials
• Wonderful symmetric varieties and Schubert polynomials
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Stanley symmetric functions for signed involutions

This page was built for publication: Involution words: counting problems and connections to Schubert calculus for symmetric orbit closures