On simple modules with singular highest weights for so2l+1(K)
so2l+1(K) үшiн сингуляр үлкен салмақты жәй модульдер туралы
О простых модулях со старшим сингулярным весом для so2l+1(K)
Ibraev Sh.Sh. Seitmuratov A.Zh. Kainbayeva L.S.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#105Issue 152 - 65 pp.
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.
algebraic group , Jantzen filtration , Lie algebra , simple module , Weyl module
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Korkyt Ata Kyzylorda University, Kyzylorda, Kazakhstan
Korkyt Ata Kyzylorda University
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