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A
combinatorial description of the centralizer algebras
connected to the Links–Gould invariant
Cristina Ana-Maria Anghel |
|
Algebraic & Geometric Topology 21 (2021) 1553–1593
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Abstract |
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We study the tensor powers of the standard representation of the super-quantum algebra , focusing on the rings of its algebra endomorphisms, called centralizer algebras and denoted by . Their dimensions were conjectured by I Marin and E Wagner (Adv. Math. 248 (2013) 1332–1365). We prove this conjecture, describing the intertwiner spaces from a semisimple decomposition as sets consisting of certain paths in a planar lattice with integer coordinates. Using this model, we present a matrix unit basis for the centralizer algebra , by means of closed curves in the plane, which are included in the lattice with integer coordinates. |
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Keywords
quantum algebra, representation theory, centralizer
algebras
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Mathematical Subject Classification
Primary: 57K10
Secondary: 16T20, 17B37, 20F36, 57K31
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References |
Publication
Received: 3 July 2020
Revised: 16 November 2020
Accepted: 27 December 2020
Published: 11 August 2021
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Authors |
| Cristina Ana-Maria Anghel | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| https://www.maths.ox.ac.uk/people/cristina.palmer-anghel | |
