{"issue":"3","oa":1,"article_type":"original","main_file_link":[{"url":"https://arxiv.org/abs/1708.08013","open_access":"1"}],"publication_status":"published","status":"public","publication":"Annales Scientifiques de l'Ecole Normale Superieure","volume":53,"external_id":{"isi":["000592182600004"],"arxiv":["1708.08013"]},"citation":{"ama":"Su C, Zhao G, Zhong C. On the K-theory stable bases of the springer resolution. <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. 2020;53(3):663-671. doi:<a href=\"https://doi.org/10.24033/asens.2431\">10.24033/asens.2431</a>","apa":"Su, C., Zhao, G., &#38; Zhong, C. (2020). On the K-theory stable bases of the springer resolution. <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. Société Mathématique de France. <a href=\"https://doi.org/10.24033/asens.2431\">https://doi.org/10.24033/asens.2431</a>","chicago":"Su, C., Gufang Zhao, and C. Zhong. “On the K-Theory Stable Bases of the Springer Resolution.” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. Société Mathématique de France, 2020. <a href=\"https://doi.org/10.24033/asens.2431\">https://doi.org/10.24033/asens.2431</a>.","ista":"Su C, Zhao G, Zhong C. 2020. On the K-theory stable bases of the springer resolution. Annales Scientifiques de l’Ecole Normale Superieure. 53(3), 663–671.","ieee":"C. Su, G. Zhao, and C. Zhong, “On the K-theory stable bases of the springer resolution,” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>, vol. 53, no. 3. Société Mathématique de France, pp. 663–671, 2020.","short":"C. Su, G. Zhao, C. Zhong, Annales Scientifiques de l’Ecole Normale Superieure 53 (2020) 663–671.","mla":"Su, C., et al. “On the K-Theory Stable Bases of the Springer Resolution.” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>, vol. 53, no. 3, Société Mathématique de France, 2020, pp. 663–71, doi:<a href=\"https://doi.org/10.24033/asens.2431\">10.24033/asens.2431</a>."},"isi":1,"abstract":[{"text":"Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in computing the quantum connection of cotangent bundle of partial flag varieties. In this paper we study the K-theoretic stable bases of cotangent bundles of flag varieties. We describe these bases in terms of the action of the affine Hecke algebra and the twisted group algebra of KostantKumar. Using this algebraic description and the method of root polynomials, we give a restriction formula of the stable bases. We apply it to obtain the restriction formula for partial flag varieties. We also build a relation between the stable basis and the Casselman basis in the principal series representations of the Langlands dual group. As an application, we give a closed formula for the transition matrix between Casselman basis and the characteristic functions.","lang":"eng"},{"text":"Les bases stables cohomologiques et K-théoriques proviennent de l’étude de la cohomologie quantique et de la K-théorie quantique. La formule de restriction pour les bases stables cohomologiques a joué un rôle important dans le calcul de la connexion quantique du fibré cotangent de variétés de drapeaux partielles. Dans cet article, nous étudions les bases stables K-théoriques de fibré cotangents des variétés de drapeaux. Nous décrivons ces bases en fonction de l’action de l’algèbre de Hecke affine et de l’algèbre de Kostant-Kumar. En utilisant cette description algébrique et la méthode des polynômes de racine, nous donnons une formule de restriction des bases stables. Nous l’appliquons\r\npour obtenir la formule de restriction pour les variétés de drapeaux partielles. Nous construisons également une relation entre la base stable et la base de Casselman dans les représentations de la série principale du groupe dual de Langlands p-adique. Comme une application, nous donnons une formule close pour la matrice de transition entre la base de Casselman et les fonctions caractéristiques. ","lang":"fre"}],"author":[{"first_name":"C.","last_name":"Su","full_name":"Su, C."},{"first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang","last_name":"Zhao"},{"first_name":"C.","full_name":"Zhong, C.","last_name":"Zhong"}],"title":"On the K-theory stable bases of the springer resolution","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"department":[{"_id":"TaHa"}],"publication_identifier":{"issn":["0012-9593"]},"year":"2020","page":"663-671","quality_controlled":"1","date_updated":"2023-08-22T09:27:57Z","oa_version":"Preprint","scopus_import":"1","type":"journal_article","day":"01","_id":"8539","publisher":"Société Mathématique de France","date_published":"2020-06-01T00:00:00Z","doi":"10.24033/asens.2431","article_processing_charge":"No","date_created":"2020-09-20T22:01:38Z","month":"06","intvolume":"        53"}