Irreducible Representations of GL_(n)(C)of Minimal Gelfand-Kirillov Dimension  

作　　者：Zhan Qiang BAI Yang Yang CHEN Dong Wen LIU Bin Yong SUN 

机构地区：[1]School of Mathematical Sciences,Soochow University,Suzhou 215006,P.R.China [2]School of Sciences,JiangnanUniversity,Wui214122,P.R.China [3]School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,P.R.China [4]Institute for Advanced Study in Mathematics,Zhejiang University,Hangzhou 310058,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第3期639-657,共19页数学学报（英文版）

基　　金：Z.Bai was supported in part by the National Natural Science Foundation of China(Grant No.12171344);the National Key R&D Program of China(Grant Nos.2018YFA0701700 and 2018YFA0701701);Y.Chen was supported in part by the National Natural Science Foundation of China(Grant No.12301035);the Natural Science Foundation of Jiangsu Province(Grant No.BK20221057);D.Liu was supported by National Key R&D Program of China(Grant No.2022YFA1005300);the National Natural Science Foundation of China(Grant No.12171421);B.Sun was supported by National Key R&D Program of China(Grant Nos.2022YFA1005300 and 2020YFA0712600);New Cornerstone Investigator Program。

摘　　要：In this article,by studying the Bernstein degrees and Goldie rank polynomials,we es-tablish a comparison between the irreducible representations of G=GL_(n)(C)possessing the minimal Gelfand-Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type(n-1,1).We give the transition matrix between the two bases for the corresponding coherent families.

关 键 词：Bernstein degree coherent continuation Gelfand-Kirillov dimension 

分 类 号：O15[理学—数学]