Centralizer construction of the Yangian of the queer Lie superalgebra

Details Centralizer construction of the Yangian of the queer Lie superalgebra Centralizer construction of the Yangian of the queer Lie superalgebra

2004-04-05

arxiv.org/abs/math/0404086v1

Mathematics

Representation Theory

24 pages

Scientific paper

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 $g=\{X(t)\in\gl_{N|N}[t]:\eta(X(t))=X(-t)\}$. 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 $q_M\subset q_{N+M}$ 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 $q_N$.

Affiliated with

Also associated with

No associations

Rating

Centralizer construction of the Yangian of the queer Lie superalgebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Centralizer construction of the Yangian of the queer Lie superalgebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Centralizer construction of the Yangian of the queer Lie superalgebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-666715