A t-Pieri rule for Hall-Littlewood P-functions and QS(t)-functions (12frg164)


(University of Pennsylvania)

Stephanie Van Willigenburg (UBC)


The "A t-Pieri rule for Hall-Littlewood P-functions and QS(t)-functions" workshop will be hosted at The Banff International Research Station.

The study of Macdonald polynomials is a dynamic and growing area of mathematics due to its connections to other areas such as algebraic geometry, representation theory and physics. Thus, understanding them is considered to be highly desirable. For example, Haiman was awarded the 2004 AMS Moore prize for his work on them and the discovery of a proof by Haglund, Haiman and Loehr of a combinatorial formula, conjectured earlier by Haglund, was a substantial breakthrough that appeared in the prestigious Journal of the American Mathematical Society. Building on the success of the BIRS Research in Teams program ``Schur quasisymmetric functions and Macdonald polynomials", the recent 2011 BIRS 5-day workshop ``Algebraic Combinatorixx", and prior to this the 2007 BIRS 5-day workshop ``Applications of Macdonald Polynomials"; Soojin Cho (Ajou University), James Haglund (University of Pennsylvania), Sarah Mason (Wake Forest University), Vasu Tewari (University of British Columbia), Stephanie van Willigenburg (University of British Columbia) and Meesue Yoo (Seoul National University) intend to further the knowledge of Macdonald polynomials by proving Yoo’s conjecture for a t-Pieri rule for Hall-Littlewood P-functions and QS(t)-functions. This will support an exciting conjecture of Haglund on nonnegative integral coefficients of a product of a Schur function and a Hall-Littlewood P-function, which are two celebrated instances of Macdonald polynomials.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).