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3 results on '"Navarro conjecture"'

1. The Navarro conjecture for the alternating groups

Author

Rishi Nath, Olivier Brunat, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), City College of New York [CUNY] (CCNY), and City University of New York [New York] (CUNY)

Subjects
Statistics::Theory, Mathematics::Number Theory, Group Theory (math.GR), Astrophysics::Cosmology and Extragalactic Astrophysics, 01 natural sciences, Combinatorics, Mathematics::Group Theory, 0103 physical sciences, FOS: Mathematics, Mathematics - Combinatorics, Representation Theory (math.RT), [MATH]Mathematics [math], 0101 mathematics, Navarro conjecture, alternating groups, Astrophysics::Galaxy Astrophysics, Mathematics, Algebra and Number Theory, Conjecture, 010102 general mathematics, Automorphism, Mckay conjecture, Combinatorics (math.CO), 010307 mathematical physics, Mathematics - Group Theory, Mathematics - Representation Theory
Abstract

International audience; Recently Navarro proposed a strengthening of the unsolved McKay conjecture using Galois automorphisms. We prove that the Navarro conjecture and its blockwise version hold for the alternating groups.

Published
2021
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2. Refinements of the Orthogonality Relations for Blocks.

Author

Sambale, Benjamin

Abstract

For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a certain cyclotomic field. After that, we use the refinements in order to give upper bounds for the number of irreducible characters (of height 0) in B. In this way we generalize results from [Héthelyi-Külshammer-Sambale, 2014]. These ideas are applied to blocks with abelian defect groups of rank 2. Finally, we address a recent conjecture by Navarro. [ABSTRACT FROM AUTHOR]

Published
2017
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3. THE NAVARRO CONJECTURE FOR THE ALTERNATING GROUPS, p = 2.

Author

NATH, RISHI

Subjects
*AUTOMORPHISMS, *GROUP theory, *ALGEBRA, *MATHEMATICAL analysis, *MATHEMATICS
Abstract

G. Navarro [10] proposed a refinement of the McKay conjecture involving a special class of automorphisms. We verify that this new conjecture holds in the case of the alternating groups for p = 2. [ABSTRACT FROM AUTHOR]

Published
2009
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