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Spinorial representations of Lie Groups

JOSHI, ROHIT (Dept. of Mathematics, 2016-08)

We solve the question: which finite-dimensional irreducible orthogonal representations of connected reductive complex Lie groups lift to the spin group? We have found a criterion in terms of the highest weight of the ...
Spinorial Representations of Symmetric and Alternating Groups

GANGULY, JYOTIRMOY (Dept. of Mathematics, 2019-02)

Representations of the symmetric groups can be thought of as homomorphisms to the orthogonal group. We give criteria for whether such a representation lifts to the Pin group, which is a two-fold cover of the orthogonal ...
Stiefel-Whitney Classes of Representations of Some Finite Groups of Lie Type

MALIK, NEHA (Dept. of Mathematics, 2022-09)

Orthogonal representations \pi of a finite group G have invariants w_i(\pi), living in the ith degree cohomology group H^i(G, Z/2Z), called Stiefel-Whitney Classes (SWCs). Their sum is known as the total SWC of \pi. There ...

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