Enumeration of concave integer partitions.
Eulerian numbers, Foulkes characters and Lefschetz characters of the symmetric group.
Finite mutation classes of coloured quivers
We show that the mutation class of a coloured quiver arising from an m-cluster tilting object associated with a finite-dimensional hereditary algebra H, is finite if and only if H is of finite or tame representation type, or it has at most two simples. This generalizes a result known for cluster categories.
Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups
We construct a subalgebra of dimension of the group algebra of the Weyl group of type containing its usual Solomon algebra and the one of : is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to . In an appendix, P. Baumann and C. Hohlweg present in an explicit and...
Generalized Dumont-Foata polynomials and alternative tableaux.
Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables.
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...
Harmonic functions on multiplicative graphs and interpolation polynomials.
Higher-dimensional cluster combinatorics and representation theory
Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite-dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection...
Hoeffding spaces and Specht modules
It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
Hoeffding spaces and Specht modules
It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
Homogeneous representations of Khovanov–Lauda Algebras
We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.
Hook length formula and geometric combinatorics.
Ideal decompositions and computation of tensor normal forms.
Identities for the number of standard Young tableaux in some -hooks.
Integrals and polygamma representations for binomial sums.
Interlaced processes on the circle
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...
Intertwining spaces associated with q-analogues of the Young symmetrizers in the Hecke algebra
Invariants of several matrices.
Inversions within restricted fillings of Young tableaux.