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This is an introductory course on the theory of Macdonald orthogonal polynomials,
double affine Hecke algebras (DAHA) and their role in modern mathematics and
physics. We will start with the basics of Macdonald theory, introducing the ring of
symmetric functions, as well as Schur functions and Macdonald polynomials. The
key point will be the connection between the Macdonald polynomials and the
Cherednik-Dunkl operators, which naturally arise in the study of quantum integrable
many-body systems, namely, the trigonometric Ruijsenaars system. We consider
nonsymmetric version of Macdonald polynomials and introduce the double affine
Hecke algebra (DAHA). We will also study the rational version, the so-called rational
Cherednik algebra, and discuss applications and connections with orthogonal
polynomials, integrable systems, and combinatorics. Similar constructions exist at the
elliptic level; these will be discussed towards the end of the course.
 RSS: Forthcoming seminars
 Lecturer
Matushko Mariya Georgievna
Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
