SVIBOR - Project code: 1-01-251

MINISTRY OF SCIENCE AND TECHNOLOGY

Strossmayerov trg 4, HR - 10000 ZAGREB
tel.: +385 1 459 44 44, fax: +385 1 459 44 69
E-mail: ured@znanost.hr

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Project code: 1-01-251


REPRESENTATION THEORY


Main researcher: KRALJEVIĆ, HRVOJE (23281)


Assistants
Type of research: basic
Duration from: 01/01/91. to 12/31/93.
Papers on project (total): 38
Institution name: Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb (37)
Department/Institute: Division for Mathematical Analysis Department of Mathematics, University of Zagreb
Address: Bijenička 30
City: 10000 - Zagreb, Croatia
Communication
Phone: 385 (0)41 432 458
Fax: 385 (0) 41 432 484
E-mail: hrk@math.hr
Summary: Classification and geometric construction of unitary irreducible representations, parametrization of primitive ideals in enveloping algebras, reducibility of induced representations of p-adic groups, construction of tempered representations, vertex-operator construction of representations of affine Lie algebras, combinatorial identities of Rogers-Ramanujan's type, character formulae for quantum groups.

Keywords: unitary representation, irreducibile representation, tempered representation, square-integrable representation, standard representation, vertex operator, Rogers-Ramanujan's identities, quantum group, primitive ideal

Research goals: (a) Representations of reductive groups (a1) Real and complex groups: Further steps in classification of unitary irreducible representations, description of the topology of the dual space and of the nonunitary dual space, parametrization of primitive ideals in enveloping algebras, geometric constructions of irreducible representations. (a2) p-adic groups: The goal of investigation is developing of techniques for construction and classification of the most important classes of irreducible representations for some series of reductive p-adic groups. These techniques are then applied to constructing new square-integrable representations. (b) Representations of affine Lie algebras: Construction of general integrable irreducible representations using vertex-operators and study of a part of anihilating ideal, combinatorial consequences of the Rogers-Ramanujan's type (from character formulae). (c) Representations of quantum groups: Classification and structure of irreducible integrable highest weight representations and character formulae for a broad class of quantum groups, combinatorial consequences.
Other information about the project.
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Last update: 10/24/95
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