There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of...

The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules--one for each real positive root for the corresponding affine root system ${ t X}_l^{(1)}$, as well as irreducible imaginary modules--one for each $l$-multiplication. The authors study imaginary modules by means of ``imaginary Schur-Weyl duality'' and...

This collection brings together studies of isotropic and anisotropic scatterers and waveguides, hydroacoustic antennas for echo sounders, frequency, pulse and transitional characteristics of loudspeakers, and oil residues in railway tanks. It also investigates numerical solutions of sound scattering problems by bodies of non-analytical forms using the boundary element method.