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 $A$ at roots of unity. For $q$ a primitive $\ell$-th root of unity we obain a non-unital imbedding of (a quotient of) the group algebra of $S_m$ into (a quotient of) the Hecke algebra $H_n(q)$ for certain $m$ and $n$. 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 $\lambda$, $\mu$ for which the decomposition number $d_{\lambda, \mu}$ 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 qq-Brauer algebras

In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-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 $A_{n-1}.$ Moreover, when $R$ is a field of arbitrary characteristic, we determine for which parameters the $q$-Brauer algebras are quasi-heredity. So the general theory of cellular algebras and quasi-hereditary algebras applies to $q$-Brauer algebras. As a consequence, we can determine all irreducible representations of $q$-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 $3\pi$ 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 ($\sim12,000\,\rm{deg}^2$) to a much larger area ($\sim\rm{21486}\,\rm{deg}^2$). This spectroscopic survey targets the most luminous quasars ($M_{1450}\le-26.5$; $m_{i}\le18.5$) at intermediate redshifts ($z\ge2.8$). Candidates are selected based on a near-infrared JKW2 color cut using WISE AllWISE and 2MASS photometry to mainly reject stellar contaminants. Photometric redshifts ($z_{\rm{reg}}$) 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 $z_{\rm{reg}}\ge2.8$ 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 $z\ge2.8$ quasars and an additional 28 quasars at lower redshifts. A total of 44 good PS-ELQS candidates remain unobserved. Including all known quasars at $z\ge2.8$, our quasar selection method has a selection efficiency of at least $77\%$. At lower declinations $-30\le\rm{Decl.}\le0$ we approximately triple the known population of extremely luminous quasars. We provide the PS-ELQS quasar catalog with a total of 592 luminous quasars ($m_{i}\le18.5$, $z\ge2.8$). 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 $B_n(q,r)$ by lifting bases for cell modules of $B_{n-1}(q,r)$ 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 $q$ and $r$, 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