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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, 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.
The stable Tamari lattice
Tue, Nov. 3 2:30pm (MATH 3…
John McHugh (CU Denver)
X
One way to understand the modular (positive characteristic) representations of a finite group G is to consider the blocks of the group. The blocks have invariants associated to them which the entire group does not possess. For example, a block determines a fusion system --- a finite category with deep connections to the homotopy theory of the classifying space of G. Further, the fusion system has attached to it a family of second cohomology classes called the Kulshammer-Puig classes of the block. I will discuss the computation of these cohomology classes for unipotent blocks of finite groups of Lie type (in non-defining characteristic). It turns out that in this case all of the Kulshammer-Puig classes are trivial in a strong way. Joint with Mandi Schaeffer Fry of the University of Denver and Justin Lynd of the University of Louisiana at Lafayette.
On the Kulshammer-Puig classes of unipotent blocks
Semistandard tableaux and (co)switching on d-complete posets