Irreducible Generalized Restricted Representations of g(Δ2)


Ibraev S.S. Kainbayeva L. Yensebayeva G.M. Ibrayeva A.A. Parmenova M.Z. Yeshmurat G.K. Abuova N.A.
December 2025Multidisciplinary Digital Publishing Institute (MDPI)

Symmetry
2025#17Issue 12

Generalized restricted representations were introduced to facilitate the study of representations of modular Lie algebras that lack a restricted structure. At present, generalized restricted representations are defined for Lie algebras of the Cartan type and for contragredient Lie algebras over fields of positive characteristic. Classifications of irreducible generalized restricted representations have been obtained for both classes of Lie algebras. However, irreducible generalized restricted representations with non-restricted highest weights, as well as their dimensions, remain largely unexplored. For contragredient Lie algebras, the dimensions of such representations are known only in the case of a three-dimensional simple algebra over a field of characteristic 2. In this paper, we study irreducible generalized restricted representations of the ten-dimensional simple contragredient Lie algebra (Formula presented.) with a Cartan matrix of (Formula presented.) over an algebraically closed field of characteristic (Formula presented.) We provide a complete classification of the irreducible generalized restricted (Formula presented.) modules and their dimensions (Theorem 1). These modules are parameterized by the fundamental weights (Formula presented.) and (Formula presented.) and by elements of the finite field (Formula presented.).

contragredient Lie algebra , generalized restricted representation , irreducible representation , simple Lie algebra

Text of the article Перейти на текст статьи

Department of Physics and Mathematics, Institute of Natural Science, Korkyt Ata Kyzylorda University, Aiteke bie St. 29A, Kyzylorda, 120014, Kazakhstan

Department of Physics and Mathematics

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026