AbstractSiegel modular forms generalize the usual elliptic modular forms and show up in many parts of mathematics: algebraic geometry, number theory and even in mathematical physics. But they are difficult to construct. We show that invariant theory enables us to efficiently construct all (vector valued) Siegel modular forms of degree two and three from from certain basic modular forms provided...
AbstractThe Deligne-Simpson problem asks for a criterion of the existence of connections on an algebraic curve with prescribed singularities at punctures. We give a solution to a generalization of this problem to G-connections on P^1 with a regular singularity and an irregular singularity (satisfying a condition called isoclinic). Here G can be any complex reductive group. Perhaps surprisingly,...
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