Yangian of the Queer Lie Superalgebra

Abstract

Take the matrix Lie superalgebra $g{l}_{N|N}$ with the standard generators $E_{ij}$ where $i,j=-N,...,-1,1,...,N$. Define an involutive automorphism of $g{l}_{N|N}$ by sending $E_{ij}$ to $E_{-i,-j}$. Then the corresponding twisted subalgebra $g$ in the polynomial current Lie superalgebra $g{l}_{N|N}[u]$, has a natural Lie co-superalgebra structure. Here we quantise the universal enveloping algebra $U(g)$ as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld. We also construct a class of irreducible representations of the quantised algebra, by introducing an appropriate analogue of the degenerate affine Hecke algebra.

AmS-TeX, 28 pages, Section 2 streamlined

References in corpus (1)

• Yang-Baxter equation in spin chains with long range interactions

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