A SIMPLE ALGORITHM FOR COMPUTING THE GLOBAL CRYSTAL BASIS OF AN IRREDUCIBLE Uq(sln)-MODULE

DOI10.1142/S0218196700000042zbMath1040.17011OpenAlexW2063352438MaRDI QIDQ4786243

Bernard Leclerc, Philippe Toffin

Publication date: 15 December 2002

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196700000042

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (15)

Constructible characters and canonical bases ⋮ Dual canonical bases and Kazhdan-Lusztig polynomials ⋮ An Algorithm for Computing the Global Basis of a Finite Dimensional IrreducibleU_q(so_2n+1) orU_q(so_2n)-Module ⋮ An Algorithm to Compute the Canonical Basis of an Irreducible Module Over a Quantized Enveloping Algebra ⋮ The \(\mathfrak{sl}_N\)-web algebras and dual canonical bases ⋮ A remark on convolution products for quiver Hecke algebras ⋮ On a conjecture about cellular characters for the complex reflection group \(G(d,1,n)\) ⋮ Bitableaux and zero sets of dual canonical basis elements ⋮ \(\mathfrak{sl}_3\)-web bases, intermediate crystal bases and categorification ⋮ Crystal bases and generalized Lascoux–Leclerc–Thibon (LLT) algorithm for the quantum affine algebra Uq(Cn(1)) ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ Constructing Canonical Bases of Quantized Enveloping Algebras ⋮ 𝔤𝔩n-webs, categorification and Khovanov–Rozansky homologies ⋮ Global crystal bases and q-Schur algebras ⋮ An algorithm for computing the global basis of an irreducible \(U_q(sp_{2n})\)-module

Cites Work

• Special bases for \(S_n\) and \(\text{GL}(n)\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras

This page was built for publication: A SIMPLE ALGORITHM FOR COMPUTING THE GLOBAL CRYSTAL BASIS OF AN IRREDUCIBLE U_q(sl_n)-MODULE