5 papers
Graded embeddings, root generated subalgebras and -systems for quasisimple Kac-Moody superalgebras
Irfan Habib, Deniz Kus, Chaithra Pilakkat
Motivated by a construction of Gorelik and Shaviv, we show that the real roots of a root generated subalgebra associated with a -system contained in the positive roots are obtai…
On the Polytope Model and Near End node Isomorphisms of Type Kirillov--Reshetikhin Crystals
Dipnit Biswas, Irfan Habib
We prove an inductive formula to construct a path from the highest weight element to any given vertex in the crystal graph of the polytope realization of the Kirillov-Reshetikhin c…
Maximal root subsystems of affine reflection systems and duality
Irfan Habib
Any maximal root subsystem of a finite crystallographic reduced root system is either a closed root subsystem or its dual is a closed root subsystem in the dual root system. In thi…
On the characterization of chordal graphs using Horn hypergeometric series
Dipnit Biswas, Irfan Habib, R. Venkatesh
Radchenko and Villegas characterized the chordal graphs by the inverse of their independence polynomials being Horn hypergeometric series in Radchenko et al. in 2021. In this paper…
Root generated subalgebras of symmetrizable Kac-Moody algebras
Irfan Habib, Deniz Kus, R. Venkatesh
The derived algebra of a symmetrizible Kac-Moody algebra $\lie g$ is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natu…