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Axioms
Special Issues
Recent Advances in Representation Theory with Applications
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Recent Advances in Representation Theory with Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 1870

Special Issue Editor

Prof. Dr. Ivan Matić

E-Mail Website
Guest Editor
School of Applied Mathematics and Informatics, University of Osijek, Trg Ljudevita Gaja 6, 31000 Osijek, Croatia
Interests: representations of classical p-adic groups; unitary dual; theta-correspondence; covering groups

Special Issue Information

Dear Colleagues,

The representation theory presents a well-studied field that has, for many years, influenced several branches in mathematics, ranging from mathematical physics to the number theory. In recent years, significant progress has been achieved in understanding both complex and Banach space representations of classical groups and of Lie algebras. This knowledge has been expanded through the development and application of several methods, such as Hecke algebra considerations, L-functions, endoscopic methods, and theta correspondence, among others. In general, several theoretical representation methods intertwine to provide a more comprehensive approach to the studied problems. Additionally, the results obtained occasionally provide a different insight into themes related to different important subjects in pure mathematics.

The main aim of this Special Issue is to provide an opportunity to present recent developments in the representation theory and its applications, and to show how the developed methods can be used and further upgraded in different situations. It covers all aspects of the representation theory, such as the structure of complex, l-adic and Banach representations, as well as those of related research areas, such as automorphic and modular forms, Lie groups, Lie algebras, and harmonic analysis on groups of the Lie type.

We invite high-quality original research papers as well as comprehensive reviews related to the proposed topic.

Prof. Dr. Ivan Matić
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • representations of reductive groups
  • automorphic forms
  • modular forms
  • L-functions
  • Lie algebras and their representations
  • representations of Clifford algebras
  • representations of finite groups
  • harmonic analysis on groups of the Lie type
  • unitary representations
  • applications of representation theory

Published Papers (2 papers)

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Research

20 pages, 356 KiB  
Article
Certain L2-Norms on Automorphic Representations of SL(2, R)
by Hongyu He
Axioms 2024, 13(2), 80; https://doi.org/10.3390/axioms13020080 - 25 Jan 2024
Viewed by 726
Abstract
Let Γ be a non-uniform lattice in SL(2,R). In this paper, we study various L2-norms of automorphic representations of SL(2,R). We bound these norms with intrinsic norms [...] Read more.
Let Γ be a non-uniform lattice in SL(2,R). In this paper, we study various L2-norms of automorphic representations of SL(2,R). We bound these norms with intrinsic norms defined on the representation. Comparison of these norms can help us understand the growth of L-functions in a systematic way. Full article
(This article belongs to the Special Issue Recent Advances in Representation Theory with Applications)
13 pages, 358 KiB  
Article
Spectral Analysis of the Adjacency Matrices for Alternating Quotients of Hyperbolic Triangle Group ▵*(3,q,r) for q < r Primes
by Sajida Younas, Sajida Kousar, Majed Albaity and Tahir Mahmood
Axioms 2023, 12(12), 1128; https://doi.org/10.3390/axioms12121128 - 15 Dec 2023
Viewed by 790
Abstract
Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane. Higman raised a question about the simplicity of [...] Read more.
Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane. Higman raised a question about the simplicity of finitely generated groups. The best known example of a simple group is the alternating group An, where n≥5. This article establishes a relation between the hyperbolic triangle group denoted as ▵*(3,7,r) and the alternating group. The approach involves employing coset diagrams to establish this connection. The construction of adjacency matrices for these coset diagrams is performed, followed by a detailed examination of their spectral characteristics. Full article
(This article belongs to the Special Issue Recent Advances in Representation Theory with Applications)
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