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This seminar covers a wide range of topics in Lie theory including (but not limited to) groups of Lie type, Lie algebras, Coxeter groups and their Hecke algebras, algebraic groups, and quantum groups, with emphasis on combinatorial and representation theoretic properties. Further information about upcoming seminars and people in the math department can be found at the CU Math Department Home Page.
Tue, Sep. 1 2:30pm (MATH 3…
Richard Green (CU)
X
A poset congruence is the analogue for partially ordered sets of a lattice congruence. If a group G acts on the underlying set of a poset P, then we call a poset congruence "G-invariant" if the G-action respects the partition of P into congruence classes. This talk will discuss specific examples where G is a Weyl group of type A or D.
This is partly based on joint work with Tianyuan Xu (University of Richmond).
Invariant poset congruences
Tue, Sep. 29 2:30pm (MATH 3…
Katrina Barron (Notre Dame University)
X
We recall some aspects of the representation theory for Lie algebras and how some number theory makes an appearance through characters for modules. We motivate why this occurs by putting this in the setting of vertex operator algebras which are the algebras that naturally arise from the geometry of Conformal Field Theory (or string theory). We discuss how analytic properties can be proved in certain settings by the construction of a modular linear differential equation, including recently in a new setting through joint work with Florencia Orosz Hunziker and Gaywalee Yamskulna.
Why should we expect number theoretic properties to arise in Lie theory and group theory? Sponsored by the Meyer Fund
Tue, Oct. 13 2:30pm (MATH 3…
Kelsey Brown (Colorado State University)
X
In the 1990's, Proctor classified the d-complete posets, which correspond to λ-minuscule elements of Weyl groups of simply laced Kac-Moody algebras. These have the Jeu de Taquin property for the natural generalization of standard Young tableaux theory to posets.
We define a notion of highest weight tableaux for several infinite families of d-complete posets. These constructions allow us to develop local algorithms for coswitching pairs of tableaux on these families, a coplactic version of tableau switching that, in the known setting of types A and B, connects naturally to Schubert calculus, crystals, and promotion and evacuation.
Semistandard tableaux and (co)switching on d-complete posets
The Tamari lattice is a poset that captures structure related to the associative law. It has importance in Catalan combinatorics, lattice theory, polyhedral geometry, and the study of the diagonal coinvariants. We unify the Tamari lattice and two of its generalizations as objects contained within a larger infinite lattice we call the stable Tamari lattice. We discuss various lattice properties as well as interesting results on height generating functions of intervals. We also study the structure and enumeration of principal lower order ideals.
Invariant poset congruences