Myungho Kim

Simplicity of heads and socles of tensor products

We prove that, for simple modules

Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux

M

Crystal bases for the quantum queer superalgebra

and

Highest Weight Modules Over Quantum Queer Superalgebra {U_q(\mathfrak {q}(n))}

N

Homotopy invariants of nonorientable 4-manifolds

over a quantum affine algebra, their tensor product

Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras III

M\otimes N

Novel method of measuring polymer melt viscosity using a short length of single screw extruder at the closed discharge state

has a simple head and a simple socle if

Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras

M\otimes M

Monoidal categorification of cluster algebras

is simple. A similar result is proved for the convolution product of simple modules over quiver Hecke algebras.

Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras IV

In this paper, we give an explicit combinatorial realization of the crystal B(\lambda) for an irreducible highest weight U_q(q(n))-module V(\lambda) in terms of semistandard decomposition tableaux. We present an insertion scheme for semistandard decomposition tableaux and give algorithms of decomposing the tensor product of q(n)-crystals. Consequently, we obtain explicit combinatorial descriptions of the shifted Littlewood-Richardson coefficients.