Bases for parametrized iterativity

Iterative Algebras for a Base

For algebras A whose type is given by an endofunctor, iterativity means that every flat equation morphism in A has a unique solution. In our previous work we proved that every object generates a free iterative algebra, and we provided a coalgebraic construction of those free algebras. Iterativity w.r.t. an endofunctor was generalized by Tarmo Uustalu to iterativity w.r.t. a “base”, i.e., a func...

A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space

Modern simulation scenarios require real-time or many-query responses from a simulation model. This is the driving force for increased efforts in Model Order Reduction (MOR) for high dimensional dynamical systems or partial differential equations (PDEs). This demand for fast simulation models is even more critical for parametrized problems. Several snapshot-based methods for basis construction ...

The Nature of Iterativity: Evidence from Lango

ESI The Erwin

Certain combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level k standard modules for affine Lie algebra sl(r,C)e are parametrized by (k, r)-admissible configurations. In this note we use Capparelli-LepowskyMilas’ method to give a new proof of linear independence of these bases, the main ingredient in the proof being the use of Dong-Lepowsky’s intertwining operators for fundamental...

(k, r)-ADMISSIBLE CONFIGURATIONS AND INTERTWINING OPERATORS

Certain combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level k standard modules for affine Lie algebra sl(r, C)̃ are parametrized by (k, r)-admissible configurations. In this note we use Capparelli-LepowskyMilas’ method to give a new proof of linear independence of these bases, the main ingredient in the proof being the use of Dong-Lepowsky’s intertwining operators for fundamental...