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Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

An exponential sum of the form sum_(n=1)^Ne^(2piiP(n)), (1) where P(n) is a real polynomial (Weyl 1914, 1916; Montgomery 2001). Writing e(theta)=e^(2piitheta), (2) a notation ...

The Weyl tensor is the tensor C_(abcd) defined by R_(abcd)=C_(abcd)+2/(n-2)(g_(a[c)R_d]b-g_(b[c)R_(d]a)) -2/((n-1)(n-2))Rg_(a[c)g_(d]b), (1) where R_(abcd) is the Riemann ...

The crystallographic point groups are the point groups in which translational periodicity is required (the so-called crystallography restriction). There are 32 such groups, ...

A group generated by the elements P_i for i=1, ..., n subject to (P_iP_j)^(M_(ij))=1, where M_(ij) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p,q,r)] ...

A sequence {x_1,x_2,...} is equidistributed iff lim_(N->infty)1/Nsum_(n<N)e^(2piimx_n)=0 for each m=1, 2, .... A consequence of this result is that the sequence {frac(nx)} is ...

A group that has a primitive group action.

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...