Alladi Ramakrishnan Hall

Covering number of some irreducible characters of the Symmetric group

Rijubrata Kundu

IMSc

In 1986, Arad, Herzog, and Chillag defined the notion of "covering number" of a non-linear irreducible character of a finite group (which may or may not exist) and subsequently defined "character covering number" of a finite group. They showed that this number exists in a non-abelian finite simple group. They made a systematic study of this notion for non-abelian finite simple groups and proved various interesting results. A. Miller recently showed that the character covering number of $S_n$ exists and it is equal to $n-1$. In this talk, we will discuss these ideas and also mention results on covering number of some irreducible characters of $S_n$ from our work (joint with Velmurugan S). The Kronecker product will naturally appear in this setting, which we will discuss as well.