May2021
Schedule for May 2021
Talk 18
Date: 04 May 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Dr Shiv Prakash Patel, IIT Delhi, India.
Title: A multiplicity one theorem for Whittaker models.
Abstract: Let $O$ be the ring of integers of a non-archimedian local field $F$ and $G=GL_n$. The uniqueness of Whittaker models of the representations of $G(F)$ plays an important role in the theory of automorphic forms. In this talk, we will discuss Whittaker models of representations of $G(O)$. On the other hand, the regular representations of $G(O)$ are useful in constructing the supercuspidal representations of $G(F)$. It turns out that only regular representations admit a Whittaker model. We discuss the uniqueness of the Whittaker models for the representations of $G(O)$. The proofs are based on the explicit construction of regular representations. This is a joint work with Pooja Singla.
Talk 19
Date: 11 May 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Professor C. S. Rajan, TIFR Mumbai, India
Title: Restrictions of representations.
Abstract: We give an introduction to some questions concerning the restriction of representations of a compact connected group to a closed, connected subgroup.
Talk 20
Date: 18 May 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Pooja Singla, IIT Kanpur, India
Title: Quasi Steinberg characters of Symmetric and Alternating groups and their double covers.
Abstract: Every finite group of Lie type has a special kind of irreducible character called Steinberg Character. This character has the property that its dimension is equal to the cardinality of a Sylow-p subgroup of G and has a specific non-zero value on all p-regular elements. This notion was extended to all finite groups by Feit. In this talk, we will discuss the classification of these and their generalizations, called quasi Steinberg characters, for the Symmetric and Alternating groups and their double covers. This talk is based on joint work with Digjoy Paul.
Talk 21
Date: 25 May 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Vipul Kakkar, Central University of Rajsthan, India
Title: Loops and Gyrogroups.
Abstract: Loops and Gyrogroups are non-associative algebraic systems. They can be regarded as the nonassociative generalizations of groups. They appear naturally in other branches of mathematics. In this talk, I will discuss the problems related to these areas. I will also discuss my ongoing work.