# Quantum torus symmetries of multicomponent modified KP hierarchy and reductions

## TL;DR

This paper constructs the multicomponent modified KP hierarchy, explores its quantum torus symmetries, and derives reduced hierarchies with Virasoro symmetries, advancing understanding of integrable systems.

## Contribution

It introduces the multicomponent modified KP hierarchy with quantum torus symmetries and develops its reductions with Virasoro symmetries, highlighting new algebraic structures.

## Key findings

- Multicomponent modified KP hierarchy constructed
- Additional symmetries form a quantum torus Lie algebra
- Reduced hierarchy exhibits Virasoro type symmetries

## Abstract

In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the constrained multicomponent modified KP hierarchy and its Virasoro type additional symmetries.