Mackey Namespace Reference

Classes
struct	Levels
	Storage of various levels of Junction/Chains. More...
class	MackeyFunctor
	A Mackey Functor. More...

Typedefs
template<typename rank_t >
using	iso_t = std::vector< dense_t< rank_t > >
	Isomorphism type of Mackey Functors. More...

Functions
template<typename group_t >
auto	transfer (const typename group_t::rank_t &, int)
	Transfer the rank to given level. More...
template<typename group_t >
auto	transfer (const typename group_t::diff_t &diff, const typename group_t::rank_t &domain, typename group_t::rank_t &domain_top, const typename group_t::rank_t &range, typename group_t::rank_t &range_top, int level)
	Transfer the differential to given level. We need the ranks both at the original level and the given level, for both domain and range. More...
template<typename group_t >
chains_t< group_t >	transfer (const chains_t< group_t > &C, int level)
template<typename group_t >
junction_t< group_t >	transfer (const junction_t< group_t > &J, int level)
	Transfer Junction to the desired level. More...
template<typename group_t , typename Derived >
Derived	transfer (const Eigen::MatrixBase< Derived > &generator, const typename group_t::rank_t &domain, const typename group_t::rank_t &range)
	Transfer generator to level given the ranks at the original level (domain) and the target level (range). More...
template<typename rank_t , typename Derived >
Derived	restriction (const Eigen::MatrixBase< Derived > &generator, const rank_t &domain, const rank_t &range)
	Restrict generator to level given the ranks at the original level (domain) and the target level (range). More...
template<typename rank_t , typename Derived >
Derived	action (const Eigen::MatrixBase< Derived > &generator, const rank_t &rank)
	Compute the Weyl group action on a generator given the rank of the group it lives in. More...
template<typename rank_t , typename T >
T	invRes (const T &generator, const rank_t &domain, const rank_t &range)
template<typename group_t >
dense_t< typename group_t::rank_t >	transfer (const Homology< typename group_t::rank_t, typename group_t::diff_t > &low, const Homology< typename group_t::rank_t, typename group_t::diff_t > &high, const typename group_t::rank_t &rank_low, const typename group_t::rank_t &rank_high)
	Writing the transfer of each generator in terms of the generators in the image. More...
template<typename group_t >
dense_t< typename group_t::rank_t >	restriction (const Homology< typename group_t::rank_t, typename group_t::diff_t > &high, const Homology< typename group_t::rank_t, typename group_t::diff_t > &low, const typename group_t::rank_t &rank_high, const typename group_t::rank_t &rank_low)
	Writing the restriction of each generator in terms of the generators in the image. More...
template<typename group_t >
dense_t< typename group_t::rank_t >	action (const Homology< typename group_t::rank_t, typename group_t::diff_t > &H, const typename group_t::rank_t &rank)
	Writing the Weyl group action on each generator in terms of the other generators. More...
template<typename rank_t >
std::ostream &	operator<< (std::ostream &, const MackeyFunctor< rank_t > &)
	Print Mackey Functor to output stream. More...

Typedef Documentation

iso_t

using iso_t = std::vector<dense_t<rank_t> >

Isomorphism type of Mackey Functors.

Function Documentation

transfer() [1/6]

auto Mackey::transfer	(	const typename group_t::rank_t &	,
		int
	)

Transfer the rank to given level.

transfer() [2/6]

auto Mackey::transfer	(	const typename group_t::diff_t &	diff,
		const typename group_t::rank_t &	domain,
		typename group_t::rank_t &	domain_top,
		const typename group_t::rank_t &	range,
		typename group_t::rank_t &	range_top,
		int	level
	)

Transfer the differential to given level. We need the ranks both at the original level and the given level, for both domain and range.

transfer() [3/6]

chains_t<group_t> Mackey::transfer	(	const chains_t< group_t > &	C,
		int	level
	)

transfer() [4/6]

junction_t<group_t> Mackey::transfer	(	const junction_t< group_t > &	J,
		int	level
	)

Transfer Junction to the desired level.

transfer() [5/6]

Derived Mackey::transfer	(	const Eigen::MatrixBase< Derived > &	generator,
		const typename group_t::rank_t &	domain,
		const typename group_t::rank_t &	range
	)

Transfer generator to level given the ranks at the original level (domain) and the target level (range).

restriction() [1/2]

Derived Mackey::restriction	(	const Eigen::MatrixBase< Derived > &	generator,
		const rank_t &	domain,
		const rank_t &	range
	)

Restrict generator to level given the ranks at the original level (domain) and the target level (range).

action() [1/2]

Derived Mackey::action	(	const Eigen::MatrixBase< Derived > &	generator,
		const rank_t &	rank
	)

Compute the Weyl group action on a generator given the rank of the group it lives in.

invRes()

T Mackey::invRes	(	const T &	generator,
		const rank_t &	domain,
		const rank_t &	range
	)

The inverse of the restriction function on a generator given the ranks at the original level (domain) and the target level (range).

Recall that free Mackey functors have injective restrictions, so we only need the generator to be in the image.

transfer() [6/6]

dense_t<typename group_t::rank_t> Mackey::transfer	(	const Homology< typename group_t::rank_t, typename group_t::diff_t > &	low,
		const Homology< typename group_t::rank_t, typename group_t::diff_t > &	high,
		const typename group_t::rank_t &	rank_low,
		const typename group_t::rank_t &	rank_high
	)

Writing the transfer of each generator in terms of the generators in the image.

restriction() [2/2]

dense_t<typename group_t::rank_t> Mackey::restriction	(	const Homology< typename group_t::rank_t, typename group_t::diff_t > &	high,
		const Homology< typename group_t::rank_t, typename group_t::diff_t > &	low,
		const typename group_t::rank_t &	rank_high,
		const typename group_t::rank_t &	rank_low
	)

Writing the restriction of each generator in terms of the generators in the image.

action() [2/2]

dense_t<typename group_t::rank_t> Mackey::action	(	const Homology< typename group_t::rank_t, typename group_t::diff_t > &	H,
		const typename group_t::rank_t &	rank
	)

Writing the Weyl group action on each generator in terms of the other generators.

operator<<()

std::ostream& Mackey::operator<<	(	std::ostream &	,
		const MackeyFunctor< rank_t > &
	)

Print Mackey Functor to output stream.