On the structure and representation theory of \(q\)-deformed Clifford algebras

DOI10.1007/s00209-023-03402-7arXiv2212.02925MaRDI QIDQ6139846

Travis Scrimshaw, Willie Aboumrad

Publication date: 19 December 2023

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.02925

zbMATH Keywords

basissemisimplequantum Clifford

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Clifford algebras, spinors (15A66) Representations of associative Artinian rings (16G10)

Cites Work

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• \(q\)-deformed Clifford algebra and level zero fundamental representations of quantum affine algebras
• On centralizer algebras for spin representations
• Webs and quantum skew Howe duality
• A quantum analogue of the first fundamental theorem of classical invariant theory
• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Combinatorics of representations of \(U_ q (\widehat{\mathfrak sl}(n))\) at \(q=0\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• The diamond lemma for ring theory
• The crystal base and Littelmann's refined Demazure character formula
• On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
• \(q\)-wedge modules for quantized enveloping algebras of classical type
• Mixed quantum skew Howe duality and link invariants of type \(A\)
• Decomposition of \(q\)-deformed Fock spaces
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras
• Heisenberg algebra, wedges and crystals
• Crystalizing the q-analogue of universal enveloping algebras
• Lie Groups
• Canonical Bases Arising from Quantized Enveloping Algebras
• Braided symmetric and exterior algebras
• Symmetry, Representations, and Invariants
• Webs and $q$-Howe dualities in types $\mathbf {BCD}$
• Clifford algebras, algebraic spinors, quantum information and applications

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