Titles and Short Summaries of the Talks

20 Algebra
Final: 2013/2/7
46 Shuhei Tsujie (Hokkaido Univ.) ♯
Norihiro Nakashima (Hokkaido Univ.)
A canonical system of basic invariants of a finite reflection group · · · · · 10
14:15–15:00
Summary: A canonical system of basic invariants of a finite reflection group is a system of basic
invariants satisfying certain differential equations. The system relates to mean value problems for
polytopes. An algorithm to compute the system was known but is not effective for finite reflection
groups of high-rank. Some researchers construct canonical systems for finite irreducible reflection
groups except type E. We give a canonical system explicitly for any finite irreducible reflection
group.
47 Toshiyuki Kikuta (Osaka Inst. of Tech.) ♯
Hirotaka Kodama (Kinki Univ.)
A congruence property of Igusa’s cuspform of weight 35 · · · · · · · · · · · · · 15
Shoyu Nagaoka (Kinki Univ.)
Summary: Igusa gave a set of generators of the graded ring of degree two Siegel modular forms.
In these generators, there are four even weight forms φ4, φ6, χ10, χ12, and only one odd weight form
χ35. Here φk is the normalized Eisenstein series of weight k and χk is a cusp form of weight k.
A purpose of this talk is to introduce a strange congruence relation of odd weight cusp form X35,
which is a suitable normalization of χ35. As a tool to confirm the congruence relation, a Sturm
type theorem for the odd weight case is also given.
48 Shingo Sugiyama (Osaka Univ.) ♯ Asymptotic behaviors of means of central values of automorphic Lfunctions
for GL(2) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Ramakrishnan and Rogawski gave an asymptotic formula for a mean of central L-values
attached to elliptic holomorphic cusp forms with prime level as the level tends to infinity. Tsuzuki
proved a result similar to that of Ramakrishnan and Rogawski for Hilbert cuspidal waveforms with
square free level. In this talk, we generalize Tsuzuki’s asymptotic formula to Hilbert cuspidal
waveforms with arbitrary level.
49 Yasuko Hasegawa (Keio Univ.) ♯ Central values of standard L-functions for Sp(2) · · · · · · · · · · · · · · · · · · · 10
Summary: We show that the central values of standard L-functions for Sp(2) to compute the
SL(2) × SL(2)-period of the residue of minimal parabolic Eisenstein series. First, we want to prove
some analytic properties of minimal parabolic Eisenstein series of weight k and degree 2 and clearly
express the residue of it. Next, we compute the period the residue to give the central values of
standard L-functions.
15:30–16:30 Award Lecture for 2012 Algebra Prize
Tomoyuki Arakawa (Kyoto Univ.) ♯ Representation theory of W-algebras
Summary: In this talk we will review the recent development in the representation theory of
W-algebras.