17,383 research outputs found
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 added to the
classificatio
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