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Centralizer construction of the Yangian of the queer Lie superalgebra | | Maxim Nazarov
; Alexander Sergeev
; | | Date: |
5 Apr 2004 | | Subject: | Representation Theory; Quantum Algebra | math.RT math.QA | | Abstract: | Consider 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 $eta$ of $gl_{N|N}$ by $eta(E_{ij})=E_{-i,-j}$. The queer Lie superalgebra $q_N$ is the fixed point subalgebra in $gl_{N|N}$ relative to the automorphism $eta$. Consider the twisted polynomial current Lie superalgebra $g={X(t)ingl_{N|N}[t]:eta(X(t))=X(-t)}$. 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 $q_Msubset q_{N+M}$ 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 $q_N$. | | Source: | arXiv, math.RT/0404086 | | Services: | Forum | Review | PDF | Favorites | |
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