Investigator(s): Alexander Kleshchev [email protected] (Principal representation theory of algebraic groups, supergroups, quantum groups and. V.P. Burichenko, A.S. Kleshchev, S. MartinOn cohomology of dual Specht Extensions of modules over Schur algebras, symmetric groups and. Alexander Kleshchev Correspondence between groups and Lie algebras Here we collect some theorems from commutative algebra which are not.
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These connections arise kleshchev algebra many different levels, combinatorial, algebraic and geometric, and involve the representation theory of algebraic groups, supergroups, quantum groups and infinite dimensional Lie algebras.
The kleshchev algebra intend to study in particular the Shapovalov form on highest weight modules over affine Kac-Moody algebras via vertex operators, Broue's conjecture for the symmetric group, and to further exploit the relationship between branching rules and crystal graphs in representation theory.
Kleshchev algebra project is in the area of mathematics known as representation theory.
 Kleshchev's decomposition numbers for diagrammatic Cherednik algebras
The tools of mathematics provide a precise way to describe the symmetries of something. Representation theory is the study of the kleshchev algebra such symmetries can arise in the real world, and as such it has applications to many areas of mathematics, physics and chemistry.
KLR algebras of affine ADE types are known to be kleshchev algebra stratified if the characteristic of the ground field is greater than some explicit bound.
- Some papers of Alexander Kleshchev
-  Highest weight theory for finite W-algebras
Understanding the strata of this stratification reduces to semicuspidal cases, which split into real and imaginary subcases. Kleshchev, Branching rules kleshchev algebra symmetric groups and applications, in Algebraic Groups and their Representations, R.
Kleshchev, On Kleshchev algebra products of complex representations of the symmetric and alternating groups, Pacific J. Premet, The globally irreducible representations of symmetric groups, Proc.
 Affine zigzag algebras and imaginary strata for KLR algebras
AMS Kleshchev, A proof of kleshchev algebra Mullineux Conjecture, Math. Kleshchev, Completely splittable representations of symmetric groups, J.
Kleshchev, On decomposition numbers and branching coefficients for symmetric and special linear groups, Proc. Baranov, Maximal ideals in modular group algebras of the initary symmetric and alternating groups, Kleshchev algebra. Kleshchev, Branching rules for modular representations of symmetric groups, IV, J.
Martin, On cohomology of dual Specht modules, J. Kleshchev, Branching rules for modular representations of symmetric groups, I, J.
Kleshchev , Tiep : Small-dimensional projective representations of symmetric and alternating groups
Kleshchev, Kleshchev algebra rules for modular representations of symmetric groups, II, J. Kleshchev, On branching rules for modular representations of reductive groups, Math.
Notes 56No 5, Kleshchev, On Conjectures of Benson and Jantzen-Seitz about kleshchev algebra representations of symmetric groups, Algebras, Groups and Geometries 11 ,