23-modular spin characters of $S_{q}$
Resumen
Character theory is a signicant 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 eld is the double cover S˜q 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 S˜q 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 S˜q for specific degrees q, particularly in the range 23 ≤ q ≤ 26 These computations are conducted over an algebraically closed eld 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
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