Seminar
Speaker: Dr Deep Makadiya (IIT Bombay)
Host: Dipendra Prasad
Title: Triangular and Unitriangular Decompositions of the Odd Unitary Group $SU_{2n+1}(R)$.
Time, day and date: 2:30:00 PM, Thursday, August 21
Venue: Room 105
Abstract: The existence of triangular and unitriangular factorizations has been extensively studied for classical groups over commutative rings. These decompositions are well understood for groups such as $\mathrm{SL}_n (R), \mathrm{SO}_n (R), \mathrm{Sp}_n(R)$, and $\mathrm{SU}_{2n}(R)$. However, the case of the odd unitary group $\mathrm{SU}_{2n+1}(R)$ has long posed difficulties, particularly over general commutative rings.
In this talk, I will present recent progress on this problem. I will begin by introducing two new classes of commutative rings—those satisfying the \emph{special stable range one} condition and those that are \emph{$\theta$-complete}. After outlining some of their key properties and giving illustrative examples, I will explain how these conditions allow us to establish triangular and unitriangular factorizations for the group $\mathrm{SU}_{2n+1}(R)$.
This is joint work with Prof. Shripad M. Garge.