Hecke algebras for the basic characters of the unitriangular group |
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Authors: | Carlos A M André |
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Institution: | Departamento de Matemática e Centro de Estruturas Lineares e Combinatórias, Faculdade de Ciências da Universidade de Lisboa, Rua Ernesto de Vasconcelos, Edifício C1, Piso 3, 1749-016 Lisboa, Portugal |
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Abstract: | Let denote the unitriangular group of degree over the finite field with elements. In a previous paper we obtained a decomposition of the regular character of as an orthogonal sum of basic characters. In this paper, we study the irreducible constituents of an arbitrary basic character of . We prove that is induced from a linear character of an algebra subgroup of , and we use the Hecke algebra associated with this linear character to describe the irreducible constituents of as characters induced from an algebra subgroup of . Finally, we identify a special irreducible constituent of , which is also induced from a linear character of an algebra subgroup. In particular, we extend a previous result (proved under the assumption where is the characteristic of the field) that gives a necessary and sufficient condition for to have a unique irreducible constituent. |
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Keywords: | Unitriangular group irreducible character basic character |
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