Hecke algebras of finite type are cellular

Let \cH be the one-parameter Hecke algebra associated to a finite Weyl group $W$, defined over a ground ring in which ``bad'' primes for $W$ are invertible. Using deep properties of the Kazhdan--Lusztig basis of \cH and Lusztig's \ba-function, we show that \cH has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of ``Specht modules'' for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types $A_n$ and $B_n$.Comment: 14 pages; added reference

Hecke algebras with unequal parameters and Vogan's left cell invariants

In 1979, Vogan introduced a generalised $\\tau$ -invariant for characterising primitive ideals in enveloping algebras. Via a known dictionary this translates to an invariant of left cells in the sense of Kazhdan and Lusztig. Although it is not a complete invariant, it is extremely useful in describing left cells. Here, we propose a general framework for defining such invariants which also applies to Hecke algebras with unequal parameters.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1405.573

Affine cellularity of affine Hecke algebras of rank two

We show that affine Hecke algebras of rank two with generic parameters are affine cellular in the sense of Koenig-Xi.Comment: 24 pages, 4 figures and 14 tables. New version: added references, corrected typos. Final versio

On Kazhdan-Lusztig cells in type B

32 pagesWe prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type $B$ are unions of combinatorial cells (defined using the domino insertion algorithm)

Affine Deligne-Lusztig varieties in affine flag varieties

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.Comment: 44 pages, 4 figures. Minor changes to font, references, and acknowledgments. Improved introduction, other improvements in exposition, and two new figures added, for a total of

X-ray absorption spectroscopy on layered cobaltates Na_xCoO_2

Measurements of polarization and temperature dependent soft x-ray absorption have been performed on Na_xCoO_2 single crystals with x=0.4 and x=0.6. They show a deviation of the local trigonal symmetry of the CoO_6 octahedra, which is temperature independent in a temperature range between 25 K and 372 K. This deviation was found to be different for Co^{3+} and Co^{4+} sites. With the help of a cluster calculation we are able to interpret the Co L_{23}-edge absorption spectrum and find a doping dependent energy splitting between the t_{2g} and the e_g levels (10Dq) in Na_xCoO_2.Comment: 7 pages, 8 figure

Temperature-driven reorganization of electronic order in CsV3_3Sb5_5

We report a temperature dependent x-ray diffraction study of the electronic ordering instabilities in the kagome material CsV$_3$Sb$_5$. Our measurements between 10 K and 120 K reveal an unexpected reorganization of the three-dimensional electronic order in the bulk of CsV$_3$Sb$_5$: At 10 K, a 2x2x2 superstructure modulation due to electronic order is observed, which upon warming changes to a 2x2x4 superstructure at 60 K. The electronic order-order transition discovered here involves a change in the stacking of electronically ordered V$_3$Sb$_5$-layers and agrees perfectly with anomalies previously observed in magneto-transport measurements. This implies that the temperature dependent three-dimensional electronic order plays a decisive role for transport properties, which are related to the Berry-curvature of the V-bands. Our data also show that the bulk electronic order in CsV$_3$Sb$_5$ breaks the 6-fold rotational symmetry of the underlying $P6/mmm$ lattice structure.Comment: 5 pages, 3 figure

Effect of Zn and Ni impurities on the quasiparticle renormalization in Bi-2212

The Cu substitution by Zn and Ni impurities and its influence on the mass renormalization effects in angle resolved photoelectron spectra (ARPES) of Bi-2212 is addressed. We show that the nonmagnetic Zn atoms have much stronger effect both in nodal and antinodal parts of the Brillouin zone than magnetic Ni. The observed changes are consistent with the behaviour of the spin resonance mode as seen by inelastic neutron scattering in YBCO. This strongly suggests that the "peak-dip-hump" and the "kink" in ARPES on the one side and neutron resonance on the other are closely related features.Comment: 4 pages, 3 figure

Constituents of the "kink" in high-Tc cuprates

Applying the Kramers-Kronig consistent procedure, developed earlier, we investigate in details the formation of the quasiparticle spectrum along the nodal direction of high-Tc cuprates. The heavily discussed "70 meV kink" on the renormalized dispersion exhibits a strong temperature and doping dependence when purified from structural effects. This dependence is well understood in terms of fermionic and bosonic constituents of the self-energy. The latter follows the evolution of the spin-fluctuation spectrum, emerging below T* and sharpening below Tc, and is the main responsible for the formation of the kink in question.Comment: revte