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## 第82回 2017年3月17日 14:00〜15:30

Alexander Ivanov（Imperial College London）「Calculating the rank of an element of an association scheme」

Within the axiomatic approach (which goes under the name Majorana Theory) to the
Monster group and its 196,884-dimensional algebra the following type of problems
arose. Given a matrix which is an element of an association scheme, it is necessary
to decide on the positivity of the eigenvaulues and on the multiplicity of the zero
eigenvalue. M. Mainardis, C. Franchi and the speaker had proposed a method to deal
with each of the idempotents of the association scheme separately. The most striking
application of this technique was the proof that the highest degree of a
2A-generated alternating subgroup in the Monster is 12.