Steven N. Karp

collaborators

6 papers

math.RT2026

Universal PlÃ¼cker coordinates for the Wronski map and positivity in real Schubert calculus

Steven N. Karp, Kevin Purbhoo

Given a $d$ -dimensional vector space $V \subset C [u]$ of polynomials, its Wronskian is the polynomial $(u + z_{1}) \dots (u + z_{n})$ whose zeros $- z_{i}$ are the points of $\m…

math.CO2026

Totally nonnegative maximal tori and opposed Bruhat intervals

Grant T. Barkley, Steven N. Karp

Lusztig (2024) recently introduced the space $T_{> 0}$ of totally positive maximal tori of an algebraic group $G$ . Each such torus is the intersection of a totally positiv…

math.CA2025

Zero-free sector of the Wronski map on the totally nonnegative Grassmannian

Steven N. Karp

A classical result states that if $f (z)$ is a polynomial of degree at most $n$ with nonnegative coefficients, then $f (z)$ has no zeros in the sector $∣ ar g (z) ∣ < \frac{I ¨}{} n$ of the…

math.CV2025

Positivity and universal PlÃ¼cker coordinates for spaces of quasi-exponentials

Steven N. Karp, Evgeny Mukhin, Vitaly Tarasov

A quasi-exponential is an entire function of the form $e^{c u} p (u)$ , where $p (u)$ is a polynomial and $c \in C$ . Let $V = \langle e^{h_1u}p_1(u), \dots, e^{h_Nu}p_N(u) \ran…

math.CO2025

Richardson tableaux and components of Springer fibers equal to Richardson varieties

Steven N. Karp, Martha E. Precup

Motivated by the study of Springer fibers and their totally nonnegative counterparts, we define a new subset of standard tableaux called Richardson tableaux. We characterize Richar…

math.CO2025

q-Whittaker functions, finite fields, and Jordan forms

Steven N. Karp, Hugh Thomas

The $q$ -Whittaker function $W_{λ} (x; q)$ associated to a partition $λ$ is a $q$ -analogue of the Schur function $s_{λ} (x)$ , and is defined as the $t = 0$ specialization o…