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Projects / Programmes source: ARIS

The Terwilliger algebra of a Q-polynomial distance-regular graph, Leonard pairs and Leonard triples

Research activity

Code Science Field Subfield
1.01.04  Natural sciences and mathematics  Mathematics  Algebra 

Code Science Field
P110  Natural sciences and mathematics  Mathematical logic, set theory, combinatories 
Keywords
distance-regular graph, Q-polynomial property, Terwilliger algebra, Leonard pairs, Leonard triples
Evaluation (rules)
source: COBISS
Researchers (1)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  21656  PhD Štefko Miklavič  Mathematics  Head  2007 - 2008  201 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  1669  University of Primorska, Andrej Marušič Insitute  Koper  1810014007  10,886 
Abstract
We will study the Terwilliger algebras of the Q-polynomial distance-regular graphs. One of our main goals will be to describe the irreducible modules with endpoint 1 of Terwilliger algebras of certain families of Q-polynomial distance-regular graphs. Furthermore, we will investigate the connection between thin irreducible modules of Terwilliger algebras and certain algebraic objects known as Leonard pairs and Leonard triples. The proposed project is at the core of the current trend in the research of Terwilliger algebras and Q-polynomial distance-regular graphs. Expected results of the proposed project would contribute to a common effort of the mathematical community to understand the Terwilliger algebra of a Q-polynomial distance-regular graph.
Significance for science
In the last few decades the number of papers on Terwilliger algebras has grown significantly. The proposed project is at the core of the current trend in the research of Terwilliger algebras and Q-polynomial distance-regular graphs. The results of the project contribute to a common effort of the mathematical community to understand the Terwilliger algebra of Q-polynomial distance-regular graph. The knowledge and experience obtained in the course of the project help us to keep in touch with trends in modern mathematics. All the results obtained during our cooperation are already published (or will be published) in highly respected mathematical journals and were presented at various international combinatorial conferences and seminars. Furthermore, the researchers from Slovenia were exposed to some of the finest and leading experts in the field which help deepen and broaden their research interests, thus bringing their own research to a higher level. Also, the theory of Terwilliger algebras is not as well known to the Slovenian mathematical community as it should be. We promote this theory by presenting the results of the project in seminars in Slovenia.
Significance for the country
With the proposed project Slovenia will keep in touch with modern trends in mathematics. Also, the proposed project is important for Slovenia because of it helps to create good quality, world comparable School of Mathematics in the newly established Faculty of mathematics, natural science and information technologies at University of Primorska. The fact that some of the investigators involved in the project are employed at the above mentioned faculty, an overal improvement of the research quality at this faculty may be expected.
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