107 research outputs found
Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
We construct an explicit isomorphism between blocks of cyclotomic Hecke
algebras and (sign-modified) Khovanov-Lauda algebras in type A. These
isomorphisms connect the categorification conjecture of Khovanov and Lauda to
Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally
graded, which allows us to exhibit a non-trivial Z-grading on blocks of
cyclotomic Hecke algebras, including symmetric groups in positive
characteristic.Comment: 32 pages; minor changes to section
Completely splittable representations of affine Hecke-Clifford algebras
We classify and construct irreducible completely splittable representations
of affine and finite Hecke-Clifford algebras over an algebraically closed field
of characteristic not equal to 2.Comment: 39 pages, v2, added a new reference with comments in section 4.4,
added two examples (Example 5.4 and Example 5.11) in section 5, mild
corrections of some typos, to appear in J. Algebraic Combinatoric
Decomposition numbers for abelian defect RoCK blocks of double covers of symmetric groups
We calculate the (super)decomposition matrix for a RoCK block of a double
cover of the symmetric group with abelian defect, verifying a conjecture of the
first author. To do this, we exploit a theorem of the second author and Livesey
that a RoCK block is Morita superequivalent to a wreath
superproduct of a certain quiver (super)algebra with the symmetric group
. We develop the representation theory of this wreath
superproduct to compute its Cartan invariants. We then directly construct
projective characters for to calculate its decomposition
matrix up to a triangular adjustment, and show that this adjustment is trivial
by comparing Cartan invariants
Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality
We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like "local" objects, which replace wreath products of Brauer tree algebras in the context of the Broué abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath products of zigzag algebras and imaginary semicuspidal quotients of affine KLR algebras
The Debye'S Potentials Utilization in the Three-Dimensional Problems of the Radiation and Propagation of the Elastic Waves
Abstract Are studied internal and external tasks of radiat ion of a sound by the elastic bodies, excit ing by the harmonic point source, imitating turbulent pulsation of a flo w of a liquid. The angular characteristics of radiat ion of a hollow spheroidal shell are calcu lated. The characteristic equations of the axial three-d imensional flexural waves in the hollow cylindrical shell and cylindrical bar are received with the help of Debye's potentials. The phase velocities of the various forms of these waves for shells and for cylindrical bar are calculated
Affine zigzag algebras and imaginary strata for KLR algebras
KLR algebras of affine ADE types are known to be properly stratified if the characteristic of the ground field is greater than some explicit bound. Understanding the strata of this stratification reduces to semicuspidal cases, which split into real and imaginary subcases. Real semicuspidal strata are well-understood. We show that the smallest imaginary stratum is Morita equivalent to Huerfano-Khovanov's zigzag algebra tensored with a polynomial algebra in one variable. We introduce affine zigzag algebras and prove that these are Morita equivalent to arbitrary imaginary strata if the characteristic of the ground field is greater than the bound mentioned above
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