An automaton-theoretic approach to the representation theory of quantum algebras

DOI10.1016/j.aim.2009.08.013zbMath1228.05298arXiv0901.4707OpenAlexW2963571572MaRDI QIDQ1047663

J. Lutley, Stephane Launois, Jason P. Bell

Publication date: 5 January 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.4707

zbMATH Keywords

automataquantum matricesprimitive idealsperfect matchingsPfaffiansCauchon diagrams

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Ring-theoretic aspects of quantum groups (16T20)

Related Items (2)

The Dixmier-Moeglin equivalence for Leavitt path algebras. ⋮ Enumeration of \(\mathcal H\)-strata in quantum matrices with respect to dimension

Cites Work

• Enumeration of totally positive Grassmann cells
• Permutation tableaux and permutation patterns
• Dimension and enumeration of primitive ideals in quantum algebras.
• Matching theory
• Lectures on algebraic quantum groups
• Prime spectrum of \(O_q(M_n(k))\): canonical image and normal separation
• Bijections between pattern-avoiding fillings of Young diagrams
• Tableaux combinatorics for the asymmetric exclusion process
• Bijections for permutation tableaux
• Primitive ideals and automorphisms of quantum matrices.
• Prime Factor Algebras of the Coordinate Ring of Quantum Matrices
• The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras
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