Centralizer construction of the Yangian of the queer Lie superalgebra

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dc.creatorNazarov, Maxim
dc.creatorSergeev, Alexander
dc.date2004-04-05
dc.date.accessioned2026-07-07T05:07:07Z
dc.date.available2026-07-07T05:07:07Z
dc.descriptionConsider the complex matrix Lie superalgebra $gl_{N|N}$ with the standard generators $E_{ij}$ where $i,j=-N,...,-1,1,...,N$. Define an involutive automorphism $η$ of $gl_{N|N}$ by $η(E_{ij})=E_{-i,-j}$. The queer Lie superalgebra $q_N$ is the fixed point subalgebra in $gl_{N|N}$ relative to the automorphism $η$. Consider the twisted polynomial current Lie superalgebra $g=\{X(t)\in\gl_{N|N}[t]:η(X(t))=X(-t)\}$. The enveloping algebra $U(g)$ of the Lie superalgebra $g$ has a deformation, called the Yangian of $q_N$. For each $M=1,2,...$ denote by $A_N^M$ the centralizer of $q_M\subset q_{N+M}$ in the superalgebra $U(q_{N+M})$. We describe the projective limit of the sequence of centralizer algebras $A_N^1,A_N^2,...$ in terms of the Yangian of $q_N$.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0404086
dc.identifierhttp://arxiv.org/abs/math/0404086
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70735
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleCentralizer construction of the Yangian of the queer Lie superalgebra
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