| takedas(@math.sci.osaka-u.ac.jp) | |
| Research |
number theory, representation theory |
| Keywords | automorphic representations, automorphic forms, representations of p-adic groups |
| URL | https://sites.google.com/view/grothendieck-jr |
One of the important objects of study in modern number theory is automorphic representations and their L-functions. An automorphic representation is a representation of a certain matrix group, normally known as reductive group, and considered as a vast generalization of classical modular forms. An automorphic representation further decomposes into their local counterparts, which are representations of reductive groups over local fields, in particular p-adic groups. I have been studying various relations among these representations, especially by using the theory known as theta correspondence. The theory of theta correspondence allows one to construct a representation of one group out of another, and thus to compare representations of different groups. Using this theory, I have obtained numerous interesting results in the theory of automorphic representations and their related themes.
