Title: Partition identities and crystal bases
Speaker: Dr Jehanne Dousse, Université Claude Bernard Lyon 1 (UCBL)
The talks will be held virtually this semester via Microsoft Teams. Link to join the meeting is given below. All are welcome.
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A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. A Rogers-Ramanujan type identity is a theorem stating that for all n, the number of partitions of n satisfying some difference conditions equals the number of partitions of n satisfying some congruence conditions. In the 1980's, Lepowsky and Wilson established a connection between the Rogers-Ramanujan identities and representation theory. Other representation theorists have then extended their method and obtained new identities yet unknown to combinatorialists, and Primc introduced a new method in connection with crystal base theory. After a general introduction on partitions and their generating functions, we will show how one can use combinatorial techniques to prove partition identities and character formulas from crystal base theory.
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