Poincare series of subsets of affine Weyl groups

In this note, we identify a natural class of subsets of affine Weyl groups whose Poincare series are rational functions. This class includes the sets of minimal coset representatives of reflection subgroups. As an application, we construct a generalization of the classical length-descent generating function, and prove its rationality.Comment: 7 page

Equidistribution of negative statistics and quotients of Coxeter groups of type B and D

We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Sch\"utzenberger, Gessel, and Roselle on various distributions of inversion number, major index, and descent number. In order to show our results we provide caracterizations of the systems of minimal coset representatives of Coxeter groups of type B and D.Comment: 18 pages, 2 figure

Abacus models for parabolic quotients of affine Weyl groups

We introduce abacus diagrams that describe minimal length coset representatives in affine Weyl groups of types B, C, and D. These abacus diagrams use a realization of the affine Weyl group of type C due to Eriksson to generalize a construction of James for the symmetric group. We also describe several combinatorial models for these parabolic quotients that generalize classical results in affine type A related to core partitions.Comment: 28 pages, To appear, Journal of Algebra. Version 2: Updated with referee's comment

Heterotic Coset Models and (0,2) String Vacua

A Lagrangian definition of a large family of (0,2) supersymmetric conformal field theories may be made by an appropriate gauge invariant combination of a gauged Wess-Zumino-Witten model, right-moving supersymmetry fermions, and left-moving current algebra fermions. Throughout this paper, use is made of the interplay between field theoretic and algebraic techniques (together with supersymmetry) which is facilitated by such a definition. These heterotic coset models are thus studied in some detail, with particular attention paid to the (0,2) analogue of the N=2 minimal models, which coincide with the `monopole' theory of Giddings, Polchinski and Strominger. A family of modular invariant partition functions for these (0,2) minimal models is presented. Some examples of N=1 supersymmetric four dimensional string theories with gauge groups E_6 X G and SO(10) X G are presented, using these minimal models as building blocks. The factor G represents various enhanced symmetry groups made up of products of SU(2) and U(1).Comment: 53 pages, harvmac (Corrections made to spectra of E_6 examples. Other minor changes.

Coset Decompositions of Space Groups: Applications to Domain Structure Analysis

Left- and double-coset decompositions of space groups are systematically analysed by putting the emphasis on the introduction of special auxiliary groups. An algorithm is tailored to exploit the specific structure of space groups. The new results are, amongst others, an efficient alternative method to determine for space groups minimal sets of double-coset representatives and a general formula that gives the structure and number of left cosets that are contained in double cosets. Left-coset and double-coset decompositions of space groups are exploited in domain structure analysis

Fermionic UV completions of Composite Higgs models

We classify the four-dimensional purely fermionic gauge theories that give a UV completion of composite Higgs models. Our analysis is at the group theoretical level, addressing the necessary (but not sufficient) conditions for the viability of these models, such as the existence of top partners and custodial symmetry. The minimal cosets arising are those of type SU(5)/SO(5) and SU(4)/Sp(4). We list all the possible "hyper-color" groups allowed and point out the simplest and most promising ones.Comment: 15 pages, 4 tables; V2 Comments and references added. To appear in JHEP. V3 Coset of type $SU(4)\times SU(4)'/SU(4)_D$ added to the classificatio