2004/04/05 by Maxim Nazarov, Nazarov, Maxim, Alexander Sergeev +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0404086
24 pages
arxiv created 2004/04/05 · arxiv updated 2009/12/01
Consider the complex matrix Lie superalgebra glN|N with the standard generators Eij where i,j=-N,...,-1,1,...,N. Define an involutive automorphism η of glN|N by η(Eij)=E-i,-j. The queer Lie superalgebra qN is the fixed point subalgebra in glN|N relative to the automorphism η. Consider the twisted polynomial current Lie superalgebra g=\X(t)∈\glN|N[t]:η(X(t))=X(-t)\. The enveloping algebra U(g) of the Lie superalgebra g has a deformation, called the Yangian of qN. For each M=1,2,... denote by ANM the centralizer of qM⊂ qN+M in the superalgebra U(qN+M). We describe the projective limit of the sequence of centralizer algebras AN1,AN2,... in terms of the Yangian of qN.