# Cyclotomic quiver Hecke algebras and Hecke algebra of $G(r,p,n)$

Salim Rostam
### Résumé

Given a quiver automorphism with nice properties, we give a presentation of the fixed point subalgebra of the associated cyclotomic quiver Hecke algebra. Generalising an isomorphism of Brundan and Kleshchev between the cyclotomic Hecke algebra of type $G(r, 1, n)$ and the cyclotomic quiver Hecke algebra of type $A$, we apply the previous result to find a presentation of the cyclotomic Hecke algebra of type $G(r, p, n)$ which looks very similar to the one of a cyclotomic quiver Hecke algebra. In addition, we give an explicit isomorphism which realises a well-known Morita equivalence between Ariki–Koike algebras.

Publication

*Transactions of the American Mathematical Society* **371** no. 6 (2019) 3877–3916