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Convention -- tableau basis convention used by PieriMaps' overhauled functions

Description

An option accepted by pieri, lrMap, applyLR, pureFree, and verifyWellDefined. Possible values: Use verifyWellDefined to verify that the chosen-convention map respects the appropriate straightening relations.
i1 : P = QQ[a,b,c];
i2 : pieri({2,1}, {1}, P, Convention => "Row")

o2 = | 2a 0  b 0 c  0 0  0 |
     | 0  2a 0 b 0  c 0  0 |
     | 0  0  0 a -a 0 2b c |

             3      8
o2 : Matrix P  <-- P
i3 : pieri({2,1}, {1}, P, Convention => "Filling")

o3 = | 3/2a 3/2b c     0    1/2c 0    0    0    |
     | 0    0    1/2b  3/2a b    3/2c 0    0    |
     | 0    0    -1/2a 0    1/2a 0    3/2b 3/2c |

             3      8
o3 : Matrix P  <-- P

See also

Functions with optional argument named Convention:

  • applyDualLR(...,Convention=>...) -- see applyDualLR -- apply dualLR to a single basis pair (T_nu, T_mu)
  • applyDualPieri(...,Convention=>...) -- see applyDualPieri -- apply dualPieri to a single basis pair (poly, T_lambda)
  • applyDualPieriColumn(...,Convention=>...) -- see applyDualPieriColumn -- apply dualPieriColumn to a single basis pair (wedge_poly, T_lambda)
  • applyLR(...,Convention=>...) -- see applyLR -- apply Psi_Q to a single tableau of shape lambda
  • applyPieri(...,Convention=>...) -- see applyPieri -- apply pieri to a single source tableau T_mu
  • applyPieriColumn(...,Convention=>...) -- see applyPieriColumn -- apply pieriColumn to a single source tableau T_mu
  • dualLR(...,Convention=>...) -- see dualLR -- GL-equivariant projection S_nu V ⊗ S_mu V --> S_lambda V at a chosen LR tableau
  • dualPieri(...,Convention=>...) -- see dualPieri -- GL-equivariant projection Sym^d V ⊗ S_lambda V --> S_mu V
  • dualPieriColumn(...,Convention=>...) -- see dualPieriColumn -- GL-equivariant projection wedge^d V ⊗ S_lambda V --> S_mu V
  • lrMap(...,Convention=>...) -- see lrMap -- GL(V)-equivariant Littlewood-Richardson inclusion
  • pieri(...,Convention=>...) -- see pieri -- computes a matrix representation for a Pieri inclusion of representations of a general linear group
  • pieriColumn(...,Convention=>...) -- see pieriColumn -- native column-form (vertical-strip) Pieri inclusion
  • pureFree(...,Convention=>...) -- see pureFree -- computes a GL(V)-equivariant map whose resolution is pure, or the reduction mod p of such a map
  • verifyEquivariant(...,Convention=>...) -- see verifyEquivariant -- rigorously verify GL_n-equivariance of a Schur-rep matrix
  • verifyWellDefined(...,Convention=>...) -- see verifyWellDefined -- verify an LR map respects the chosen convention's straightening relations

For the programmer

The object Convention is a symbol.


The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/PieriMaps/doc.m2:659:0.