News release

An SCMS paper was published online by 《Inventiones Mathematicae》

Top mathematical journal Inventiones Mathematicae has recently online published the paper “Homological branching law for (GL_{n+1}(F),GL_n(F)): projectivity and indecomposability" (https://doi.org/10.1007/s00222-021-01033-5). It is authored by Kei Yuen Chan, a young researcher (eq. assistant professor) at the Shanghai Center for Mathematical Sciences. It is the fifth paper published in a world top journal authored by a faculty at our center.

 

This paper studied the branching laws of general linear groups, which is one of the fundational problems in the representation theory. It is closely related to several important research subjects, such as the important Gan-Gross-Prasad conjectures. The paper successfully determined when an irreducible representation restricted from GL(n+1) to GL(n) is projective, described the indecomposable components of a restricted representation, and characterized the submodule branching law. The breakthrough came after the discovery of an asymmetric property of a Bernstein-Zelevinsky filtration and its dual. This property is expected to have further applications.

 

Dr. Kei Yuen Chan studied in the University of Hong Kong from 2004 to 2010 and obtained bachelor's and master's degrees. He received his Ph.D. from the University of Utah in 2014, worked as postdoctoral fellow at University of Amsterdam and later at University of Georgia, from 2015 to 2018. In 2019, Dr. Kei Yuen Chan joined Shanghai Center for Mathematical Sciences as a young researcher.

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