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Representation theory of the finite unipotent linear groups

Representation theory of the finite unipotent linear groups,N. Yan

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Representation theory of the finite unipotent linear groups   (Citations: 20)
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Published in 2001.
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    • ...While understanding the usual representation theory of Un(q) is a wild problem, Andr e [1, 2, 3, 4] and Yan [23, 24] constructed a natural approximation to the representation theory that leads to a more computable theory...
    • ...These computations require knowledge of tensor product results that were previously done by Andr e [1] for large prime and by Yan [23] for arbitrary primes...

    Nathaniel Thiem. Branching rules in the ring of superclass functions of unipotent upper...

    • ...thesis [15], N. Yan showed how the algebraic geometry of the original construction could be replaced by more elementary constructions...

    Eric Marbergand, et al. Superinduction for pattern groups

    • ...While describing the conjugacy classes or irreducible characters of Un(Fq) is a well-known wild problem, Carlos Andr´e [1, 2, 4] and Ning Yan [17, 18] have shown that certain unions of conjugacy classes (here-after superclasses) and certain characters (here-after supercharacters) have an elegant theory that is rich enough to handle some Fourier analysis problems classically needing the full character table and yet tractable enough to ...
    • ...For Un(Fq), Andr´e [1, 2, 4], Yan [17] and Arias-Castro et al [8] found that certain unions of conjugacy classes and corresponding sums of irreducible characters give a tractable, useful theory...
    • ...Andr´e [4] and Yan [17] realized that they are in fact supercharacters...

    Persi Diaconis, et al. Supercharacter formulas for pattern groups

    • ...thesis [14], N. Yan showed how the algebraic geometry of the original construction could be replaced by more elementary constructions...

    Nathaniel Thiem, et al. Restricting supercharacters of the nite group of unipotent uppertriang...

    • ...Later, in his PhD thesis [25], N. Yan showed how the “basic characters” can be obtained using more elementary methods which avoid Kazhan’s construction and the algebraic geometry involved in it. Yan’s approach is valid for an arbitrary prime, and was generalized later by P. Diaconis and M. Isaacs in...
    • ...(The subsets KD,' ⊆ Um(q) are exactly the superclasses of Um(q) as explained in [15, Appendix A]; see also the papers [4, 11], or the PhD thesis [25].)...
    • ...(The proofs in that paper use the assumption p ≥ m, but can be easily adapted for an arbitrary prime (see the thesis [25] by N. Yan); in fact, every irreducible constituent of any of the given decompositions is a supercharacter of Um(q), and thus is a Kirillov function (see [15, Theorem 5.10], or [6, Theorem 3].)...

    Carlos A. M. André, et al. Supercharacters of the Sylow p -subgroups of the finite symplectic and...

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