Open AccessOn simple modules with singular highest weights for so2l+1(K)
Author(s) -
Sh.Sh. Ibraev,
A.Zh. Seitmuratov,
L.S. Kainbayeva
Publication year - 2022
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2022m1/52-65
Subject(s) - mathematics , simple (philosophy) , representation theory , coxeter element , algebraically closed field , pure mathematics , algebraic number , simple module , algebraic group , field (mathematics) , lie algebra , algebra over a field , representation (politics) , type (biology) , coxeter group , mathematical analysis , philosophy , epistemology , politics , political science , law , ecology , biology
In this paper, we study formal characters of simple modules with singular highest weights over classical Lie algebras of type B over an algebraically closed field of characteristic p ≥ h, where h is the Coxeter number. Assume that the highest weights of these simple modules are restricted. We have given a description of their formal characters. In particular, we have obtained some new examples of simple Weyl modules. In the restricted region, the representation theory of algebraic groups and its Lie algebras are equivalent. Therefore, we can use the tools of the representation theory of semisimple and simply-connected algebraic groups in positive characteristic. To describe the formal characters of simple modules, we construct Jantzen filtrations of Weyl modules of the corresponding highest weights.