{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:25Z","timestamp":1747189705973,"version":"3.40.5"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"Portuguese Science Foundation","award":["UID\/MAT\/04721\/2013","UIDB\/04721\/2020"],"award-info":[{"award-number":["UID\/MAT\/04721\/2013","UIDB\/04721\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:p> Let [Formula: see text] be a finite-dimensional nilpotent algebra over a finite field [Formula: see text] with q elements, and let [Formula: see text]. On the other hand, let [Formula: see text] denote the algebraic closure of [Formula: see text], and let [Formula: see text]. Then [Formula: see text] is an algebraic group over [Formula: see text] equipped with an [Formula: see text]-rational structure given by the usual Frobenius map [Formula: see text], and [Formula: see text] can be regarded as the fixed point subgroup [Formula: see text]. For every [Formula: see text], the nth power [Formula: see text] is also a Frobenius map, and [Formula: see text] identifies with [Formula: see text]. The Frobenius map restricts to a group automorphism [Formula: see text], and hence it acts on the set of irreducible characters of [Formula: see text]. Shintani descent provides a method to compare F-invariant irreducible characters of [Formula: see text] and irreducible characters of [Formula: see text]. In this paper, we show that it also provides a uniform way of studying supercharacters of [Formula: see text] for [Formula: see text]. These groups form an inductive system with respect to the inclusion maps [Formula: see text] whenever [Formula: see text], and this fact allows us to study all supercharacter theories simultaneously, to establish connections between them, and to relate them to the algebraic group G. Indeed, we show that Shintani descent permits the definition of a certain \u201csuperdual algebra\u201d which encodes information about the supercharacters of [Formula: see text] for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196724500073","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T05:01:45Z","timestamp":1706677305000},"page":"207-226","source":"Crossref","is-referenced-by-count":0,"title":["Shintani descent for standard supercharacters of algebra groups"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1907-657X","authenticated-orcid":false,"given":"Carlos A. M.","family":"Andr\u00e9","sequence":"first","affiliation":[{"name":"Centro de An\u00e1lise Funcional, Estruturas, Lineares e Aplica\u00e7\u00f5es, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Edif\u00ed cio C6, Piso 2, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9510-7091","authenticated-orcid":false,"given":"Ana L.","family":"Branco Correia","sequence":"additional","affiliation":[{"name":"Centro de An\u00e1lise Funcional, Estruturas, Lineares e Aplica\u00e7\u00f5es, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Edif\u00ed cio C6, Piso 2, 1749-016 Lisboa, Portugal"},{"name":"Centro de Investiga\u00e7\u00e3o, Desenvolvimento e Inova\u00e7\u00e3o da Academia, Militar (CINAMIL) & Departamento de Ci\u00eancias, Exatas e Engenharias, Academia Militar, Av. 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