# Manchester Algebra Seminar - Dimitris Michailidis - Bases of simple representations of Temperley-Lieb algebras of type B

Starts: | 14:00 12 May 2020 |
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Ends: | 15:00 12 May 2020 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, Current University students |

Speaker: Dimitris Michailidis

Title: Bases of simple representations of Temperley-Lieb algebras of type B

Abstract: Inspired from the study of certain models in physics, Martin and Saleur defined the Temperley-Lieb algebra of type B or blob algebra as the diagrammatic two parameter generalisation of the Temperley-Lieb algebra of type A. The blob algebra can also be viewed as quotient of the Hecke algebra of type B, hence it is isomorphic to a quotient of the (graded) KLR algebra via the Brundan-Kleshchev isomorphism. It is also cellular, with cellular basis indexed by standard tableaux of one-column bipartitions. Each one-column bipartition can be embedded in the two dimensional Euclidean space and there is a bijection between standard tableaux and paths in the Euclidean space. The aim of the talk is to describe the construction of bases for the simple representations of the blob algebra. Those bases are indexed by paths in the Euclidean space with respect to the alcove geometry of affine type A_1. If time permits we shall also give a homological construction of the simple representations via the, so called, BGG resolutions.

Time: 2pm

Place: Zoom