Representations of $\mathfrak{sl}( 2,\mathbb{C} )$ on Posets and the Sperner Property
From MaRDI portal
Publication:3960891
DOI10.1137/0603026zbMath0496.06004OpenAlexW2072878295MaRDI QIDQ3960891
Publication date: 1982
Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0603026
lengthantichainsranked posetPeck posetlowering operatorraising operatorrank symmetricrank unimodalSperner posetBruhat posetsedge-labelable posetlattice of order fieldsproduct of Peck posetsrepresentations of sl(2,C)
Partial orders, general (06A06) Representation theory for linear algebraic groups (20G05) Structure theory of lattices (06B05)
Related Items (39)
A Dynkin diagram classification theorem arising from a combinatorial problem ⋮ Quantum generalized Heisenberg algebras and their representations ⋮ Unimodality of differences of specialized Schur functions ⋮ Gelfand-Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions ⋮ Peckness of edge posets ⋮ The Goldman-Rota identity and the Grassmann scheme ⋮ A \(q\)-analog of the adjacency matrix of the \(n\)-cube ⋮ Antichains in weight posets associated with gradings of simple Lie algebras ⋮ Directed and weighted majority games ⋮ Extremal properties of bases for representations of semisimple Lie algebras ⋮ Symmetric chains, Gelfand--Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme ⋮ On the cohomology of a class of nilpotent Lie algebras ⋮ Partially ordered sets and stratification ⋮ Counting Partitions inside a Rectangle ⋮ The local Kostant-PBW ordering ⋮ Towards a geometric approach to Strassen's asymptotic rank conjecture ⋮ Some applications of algebra to combinatorics ⋮ REPRESENTATIONS OF sl(2) IN THE BOOLEAN LATTICE, AND THE HAMMING AND JOHNSON SCHEMES ⋮ Generating the states of a binary stochastic system ⋮ Explicit constructions of the fundamental representations of the symplectic Lie algebras ⋮ Distance-regular graphs related to the quantum enveloping algebra of \(sl(2)\) ⋮ The Terwilliger algebra of the hypercube ⋮ Bruhat lattices, plane partition generating functions, and minuscule representations ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ Expansions of Chromatic Polynomials and Log-Concavity ⋮ Unimodal Polynomials Arising from Symmetric Functions ⋮ A combinatorial 𝔰𝔩₂-action and the Sperner property for the weak order ⋮ A combinatorial duality between the weak and strong Bruhat orders ⋮ Unnamed Item ⋮ Product evaluations of Lefschetz determinants for Grassmannians and of determinants of multinomial coefficients ⋮ The weak Bruhat order on the symmetric group is Sperner ⋮ Cyclic sieving, necklaces, and bracelets ⋮ Symplectic analogs of the distributive lattices \(L(m,n)\) ⋮ Unimodality and Lie Superalgebras ⋮ The symmetric group, ordered by refinement of cycles, is strongly Sperner ⋮ Differential Posets ⋮ The absolute orders on the Coxeter groups \(A_n\) and \(B_n\) are Sperner ⋮ The Sperner property for 132‐avoiding intervals in the weak order ⋮ Solution of a Sperner conjecture of Stanley with a construction of Gelfand
Cites Work
- A Dynkin diagram classification theorem arising from a combinatorial problem
- Product partial orders with the Sperner property
- Bruhat lattices, plane partition generating functions, and minuscule representations
- A sperner property preserved by product
- Acyclic Digraphs, Young Tableaux and Nilpotent Matrices
- Dilworth Numbers, Incidence Maps and Product Partial Orders
- Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
- Solution of Two Difficult Combinatorial Problems with Linear Algebra
- Introduction to Lie Algebras and Representation Theory
This page was built for publication: Representations of $\mathfrak{sl}( 2,\mathbb{C} )$ on Posets and the Sperner Property
