910 research outputs found
Iwahori-Hecke algebras of type A at roots of unity
In this paper, we explore the use of path idempotents for the Hecke algebra
of type at roots of unity. For a primitive -th root of unity we
obain a non-unital imbedding of (a quotient of) the group algebra of into
(a quotient of) the Hecke algebra for certain and . From this
we recover certain instances of irreducibility criteria of Dipper, James, and
Mathas, and we derive estimates on the decomposition numbers for the Hecke
algebra at roots of unity. The bounds are easily computed, provide a good
geometric picture of the pairs of diagrams , for which the
decomposition number is non-zero, and also appers to be a
useful adjunct to the exact computation of the decomposition numbers.Comment: **Second** substantial revision of previously submitted manuscript.
38 pages, TeX, with figures in EPS, requires macro BoxedEP
Cellular structure of -Brauer algebras
In this paper we consider the -Brauer algebra over a commutative
noetherian domain. We first construct a new basis for -Brauer algebras, and
we then prove that it is a cell basis, and thus these algebras are cellular in
the sense of Graham and Lehrer. In particular, they are shown to be an iterated
inflation of Hecke algebras of type Moreover, when is a field of
arbitrary characteristic, we determine for which parameters the -Brauer
algebras are quasi-heredity. So the general theory of cellular algebras and
quasi-hereditary algebras applies to -Brauer algebras. As a consequence, we
can determine all irreducible representations of -Brauer algebras by linear
algebra methods
The Extremely Luminous Quasar Survey in the Pan-STARRS 1 Footprint (PS-ELQS)
We present the results of the Extremely Luminous Quasar Survey in the
survey of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS;
PS1). This effort applies the successful quasar selection strategy of the
Extremely Luminous Survey in the Sloan Digital Sky Survey footprint
() to a much larger area
(). This spectroscopic survey targets the most
luminous quasars (; ) at intermediate redshifts
(). Candidates are selected based on a near-infrared JKW2 color cut
using WISE AllWISE and 2MASS photometry to mainly reject stellar contaminants.
Photometric redshifts () and star-quasar classifications for each
candidate are calculated from near-infrared and optical photometry using the
supervised machine learning technique random forests. We select 806 quasar
candidates at from a parent sample of 74318 sources. After
exclusion of known sources and rejection of candidates with unreliable
photometry, we have taken optical identification spectra for 290 of our 334
good PS-ELQS candidates. We report the discovery of 190 new quasars
and an additional 28 quasars at lower redshifts. A total of 44 good PS-ELQS
candidates remain unobserved. Including all known quasars at , our
quasar selection method has a selection efficiency of at least . At lower
declinations we approximately triple the known
population of extremely luminous quasars. We provide the PS-ELQS quasar catalog
with a total of 592 luminous quasars (, ). This unique
sample will not only be able to provide constraints on the volume density and
quasar clustering of extremely luminous quasars, but also offers valuable
targets for studies of the intergalactic medium.Comment: 34 pages, 10 figures, accepted to ApJ
Specht modules and semisimplicity criteria for Brauer and Birman--Murakami--Wenzl Algebras
A construction of bases for cell modules of the Birman--Murakami--Wenzl (or
B--M--W) algebra by lifting bases for cell modules of
is given. By iterating this procedure, we produce cellular bases for B--M--W
algebras on which a large abelian subalgebra, generated by elements which
generalise the Jucys--Murphy elements from the representation theory of the
Iwahori--Hecke algebra of the symmetric group, acts triangularly. The
triangular action of this abelian subalgebra is used to provide explicit
criteria, in terms of the defining parameters and , for B--M--W algebras
to be semisimple. The aforementioned constructions provide generalisations, to
the algebras under consideration here, of certain results from the Specht
module theory of the Iwahori--Hecke algebra of the symmetric group
Topological Quantum Field Theories and Operator Algebras
We review "quantum" invariants of closed oriented 3-dimensional manifolds
arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory
and Noncommutative Geometry", Sendai, November 200
Representation-theoretic derivation of the Temperley-Lieb-Martin algebras
Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the
quotients of the Hecke algebra that admit only representations corresponding to
Young diagrams with a given maximum number of columns (or rows), are obtained,
making explicit use of the Hecke algebra representation theory. Similar
techniques are used to construct the algebras whose representations do not
contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.
The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
We determine the Nakayama automorphism of the almost Calabi-Yau algebra A
associated to the braided subfactors or nimrep graphs associated to each SU(3)
modular invariant. We use this to determine a resolution of A as an A-A
bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix
detailing some long calculations. arXiv admin note: text overlap with
arXiv:1110.454
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