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Separating invariants of classical groups

Grant number: 19/10821-8
Support Opportunities:Scholarships abroad - Research
Effective date (Start): September 20, 2019
Effective date (End): February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Artem Lopatin
Grantee:Artem Lopatin
Host Investigator: Gregor Kemper
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: Technical University of Munich (TUM), Germany  


The proposed project is dedicated to some problems in Invariant Theory. Assume that the base field F is infinite of an arbitrary characteristic and G is a linear classical group, i.e. it belongs to the following list of groups: GL(n), O(n), Sp(n), SL(n), SO(n), where the characteristic of F is different from two in case G is O(n) or SO(n). Consider the action of of this group over the direct sum H of several copies of the space of matrices n x n. The set of all polynomial functions between H and F, which are constants over the orbits of the action of G over H, is called the algebra of G-invariants of matrices. Generators of this algebra are known for all groups with the exception of G=O(n) or SO(n) in case of the field of characteristic two. The notion of separating invariants was introduced by Harm Derksen e Gregor Kemper in 2002 as a simplification of the notion of generators of the algebra of invariants. Working o the proposed project, we will obtain the minimal exact degree of elements of the separating sets of invariants of matrices for groups GL(n), O(n), Sp(n) and of invariants of bilinear forms in case n is less than 5. We will construct some indecomposable invariants of the representations of the generalized quiver and investigate its properties. We will describe the generalized quivers with polynomial algebras of invariants.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
KEMPER, GREGOR; LOPATIN, ARTEM; REIMERS, FABIAN. Separating invariants over finite fields. Journal of Pure and Applied Algebra, v. 226, n. 4, . (19/10821-8)
LOPATIN, ARTEM; REIMERS, FABIAN. SEPARATING INVARIANTS FOR MULTISYMMETRIC POLYNOMIALS. Proceedings of the American Mathematical Society, v. 149, n. 2, p. 497-508, . (19/10821-8)

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