Some closed formulas for canonical bases of Fock spaces

2001/04/10 by Bernard Leclerc, Leclerc, Bernard, Hyohe Miyachi +1
Mathematics · #05E #17B #20C #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:05E #msc:17B #msc:20C

paper · pdf · doi:10.48550/arxiv.math/0104107

22 pages

openalex publication_date 2001/04/10 · arxiv created 2001/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give some closed formulas for certain vectors of the canonical bases of the Fock space representation of U_v(sl^_n). As a result, a combinatorial description of certain parabolic Kazhdan-Lusztig polynomials for affine type A is obtained.

Citations

• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras

Related

• Canonical bases of higher-level q-deformed Fock spaces
• Canonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials
• Canonical bases for Fock spaces and tensor products
• Canonical bases of q-deformed Fock spaces
• An algorithm for computing the canonical bases of higher-level q-deformed Fock spaces