Grothendieck rings of periplectic Lie superalgebras

2019/06/05 by Im, Mee Seong, Reif, Shifra, Serganova, Vera
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1906.01948

Abstract

We describe explicitly the Grothendieck rings of finite-dimensional representations of the periplectic Lie superalgebras. In particular, the Grothendieck ring of the Lie supergroup P(n) is isomorphic to the ring of symmetric polynomials in x₁^{± 1}, …, x_n^{± 1} whose evaluation x₁=x₂^-1=t is independent of t.

Related

• The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions
• Grothendieck Rings of Queer Lie Superalgebras
• Grothendieck rings of basic classical Lie superalgebras
• The primitive spectrum and category O for the periplectic Lie superalgebra
• Finite dimensional compact and unitary Lie superalgebras