23-modular spin characters of Sq

Character theory is a significant area of mathematics with diverse applications across multiple disciplines, such as computational chemistry, theoretical physics, coding theory, spectral graph theory, and information theory. One of the objects of interest in this field is the double cover Sq of the symmetric group Sq^ where q represents the degree of the group. The double cover introduces a new structural feature: a central involution b, which is an element of order 2. The irreducible characters of Sq are divided into two types: ordinary characters and spin characters. This distinction is based on whether the involution b lies in the kernel of the character (ordinary) or not (spin). The purpose of this study is to compute the modular irreducible spin characters of Sq for specific degrees q, particularly in the range 23 ≤ q ≤ 26 These computations are conducted over an algebraically closed field with characteristic $p = 23$. The results provide important insights into the modular representation theory of double covers of symmetric groups and contribute to a deeper understanding of their spin character structure in specific modular settings.