Some characters of orthogonal groups over the field of two elements

Lecture Notes in Mathematics - Proceedings of the Second International Conference on the Theory of Groups ◽

10.1007/bfb0065180 ◽

2006 ◽

pp. 298-314 ◽

Cited By ~ 1

Author(s):

J. S. Frame

Keyword(s):

Orthogonal Groups

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Low-dimensional representations of finite orthogonal groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004121000037 ◽

2021 ◽

pp. 1-22

Author(s):

KAY MAGAARD ◽

GUNTER MALLE

Keyword(s):

Orthogonal Groups ◽

Brauer Characters ◽

Low Dimensional

Abstract We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger irreducible Brauer characters have a degree roughly the square of those of the smallest non-trivial characters.

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STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748021000177 ◽

2021 ◽

pp. 1-48

Author(s):

Federico Scavia

Keyword(s):

Finite Groups ◽

Reductive Groups ◽

Orthogonal Groups ◽

De Rham Cohomology ◽

Algebraic Stacks ◽

Steenrod Operations ◽

De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

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Higher pullbacks of modular forms on orthogonal groups

Forum Mathematicum ◽

10.1515/forum-2020-0066 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Brandon Williams

Keyword(s):

Modular Forms ◽

Differential Operators ◽

Jacobi Form ◽

Siegel Modular Forms ◽

Orthogonal Groups

Abstract We apply differential operators to modular forms on orthogonal groups O ⁢ ( 2 , ℓ ) {\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature ( 2 , 2 ) {(2,2)} and ( 2 , 3 ) {(2,3)} , for which there are interpretations as Hilbert–Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

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