Grothendieck rings of periplectic Lie superalgebras

Mee Seong Im; Shifra Reif; Vera Serganova

doi:10.4310/mrl.2021.v28.n4.a8

Grothendieck rings of periplectic Lie superalgebras

Mee Seong Im, Shifra Reif, Vera Serganova

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1175-1195
Number of pages	21
Journal	Mathematical Research Letters
Volume	28
Issue number	4
DOIs	https://doi.org/10.4310/mrl.2021.v28.n4.a8
State	Published - 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4310/mrl.2021.v28.n4.a8

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title = "Grothendieck rings of periplectic Lie superalgebras",

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, . . ., xn±1 whose evaluation x1 = x2-1 = t is independent of t.",

author = "Im, \{Mee Seong\} and Shifra Reif and Vera Serganova",

year = "2021",

doi = "10.4310/mrl.2021.v28.n4.a8",

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T1 - Grothendieck rings of periplectic Lie superalgebras

AU - Im, Mee Seong

AU - Reif, Shifra

AU - Serganova, Vera

PY - 2021

Y1 - 2021

N2 - 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, . . ., xn±1 whose evaluation x1 = x2-1 = t is independent of t.

AB - 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, . . ., xn±1 whose evaluation x1 = x2-1 = t is independent of t.

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U2 - 10.4310/mrl.2021.v28.n4.a8

DO - 10.4310/mrl.2021.v28.n4.a8

M3 - مقالة

SN - 1073-2780

VL - 28

SP - 1175

EP - 1195

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 4

ER -

Grothendieck rings of periplectic Lie superalgebras

Abstract

All Science Journal Classification (ASJC) codes

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