Fusion Procedure for Cyclotomic Hecke Algebras

A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a product of two terms, one of which depends only on the shape of the multi-tableau and is proportional to the inverse of the corresponding Schur element

On representations of complex reflection groups G(m,1,n)

An inductive approach to the representation theory of the chain of the complex reflection groups G(m,1,n) is presented. We obtain the Jucys-Murphy elements of G(m,1,n) from the Jucys--Murphy elements of the cyclotomic Hecke algebra, and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. Representations of G(m,1,n) are constructed with the help of a new associative algebra whose underlying vector space is the tensor product of the group ring of G(m,1,n) with a free associative algebra generated by the standard m-tableaux.Comment: 18 page

On representations of cyclotomic Hecke algebras

An approach, based on Jucys--Murphy elements, to the representation theory of cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra) of the set of the Jucys--Murphy elements is established. A basis of the cyclotomic Hecke algebra is suggested; this basis is used to establish the flatness of the deformation without use of the representation theory

Spitzer Observations of Transient, Extended Dust in Two Elliptical Galaxies: New Evidence of Recent Feedback Energy Release in Galactic Cores

Spitzer observations of extended dust in two optically normal elliptical galaxies provide a new confirmation of buoyant feedback outflow in the hot gas atmospheres around these galaxies. AGN feedback energy is required to prevent wholesale cooling and star formation in these group-centered galaxies. In NGC 5044 we observe interstellar (presumably PAH) emission at 8 microns out to about 5 kpc. Both NGC 5044 and 4636 have extended 70 microns emission from cold dust exceeding that expected from stellar mass loss. The sputtering lifetime of this extended dust in the ~1keV interstellar gas, ~10^7 yrs, establishes the time when the dust first entered the hot gas. Evidently the extended dust originated in dusty disks or clouds, commonly observed in elliptical galaxy cores, that were disrupted, heated and buoyantly transported outward. The surviving central dust in NGC 5044 and 4636 has been disrupted into many small filaments. It is remarkable that the asymmetrically extended 8 micron emission in NGC 5044 is spatially coincident with Halpha+[NII] emission from warm gas. A calculation shows that dust-assisted cooling in buoyant hot gas moving out from the galactic core can cool within a few kpc in about ~10^7 yrs, explaining the optical line emission observed. The X-ray images of both galaxies are disturbed. All timescales for transient activity - restoration of equilibrium and buoyant transport in the hot gas, dynamics of surviving dust fragments, and dust sputtering - are consistent with a central release of feedback energy in both galaxies about 10^7 yrs ago.Comment: 13 pages. Accepted by ApJ; minor typos correcte