Analysis of the Kerov–Olshanski Algebra

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 17)


In this chapter, we investigate the algebra of polynomial functions in coordinates of Young diagrams as a nice framework in which various quantities on Young diagrams can be efficiently computed. This algebra was introduced by Kerov–Olshanski [20], analysis of which is substantially due to Ivanov–Olshanski [16]. Several systems of generators and associated generating functions are considered. It is important to understand the concrete transition rules between these generating systems, one of which is the Kerov polynomial.


Young Diagram Transition Measure Irreducible Character Homogeneous Element Plancherel Measure 

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© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

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