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Namespace LocalGL2 21 theorems

— 20 · Kirillov 1

directly in LocalGL2 20

• Iwasawa decomposition for GL₂(K) in unipotent–diagonal form LocalGL2.iwasawa_decomposition_diag 0 below · cited by 9 · depth 16
• Existence of a Cartan representative for 2× 2 matrices over a DVR LocalGL2.exists_cartanRel_cartanDiag 0 below · cited by 9 · depth 18
• Iwasawa decomposition for GL₂ over a fraction field of a DVR LocalGL2.iwasawa_decomposition 0 below · cited by 14 · depth 18
• Algebra characters of the local Hecke algebra as Satake pairs LocalGL2.existsUnique_algHom_heckeIndicator_eq 2 below · cited by 1 · depth 21
• Satake-type constant-term homomorphism for GL₂ over a discrete valuation ring LocalGL2.exists_algHom_apply_eq_finsum_indicator_heckeIndicator_diagPi_eq 1 below · cited by 1 · depth 21
• Cartan basis of the Hecke algebra of GL₂(K) LocalGL2.exists_basis_heckeIndicator_zpow 2 below · cited by 3 · depth 21
• Finiteness of the coset image of GL₂(R)g LocalGL2.finite_image_integralSubgroup_mul_singleton 2 below · cited by 7 · depth 21
• Scalar double-coset indicator is a central unit LocalGL2.heckeIndicator_diagPi_mul_localRepInf_central_isUnit 0 below · cited by 1 · depth 21
• Hecke recursion T· T_varpiⁿ=T_varpiⁿ⁺¹+q T_(varpi,varpiⁿ) for n≥ 2 LocalGL2.heckeIndicator_diagPi_mul_localRepInf_pow 0 below · cited by 4 · depth 21
• Square of the spherical Hecke operator at diag(varpi,1) LocalGL2.heckeIndicator_diagPi_mul_self 0 below · cited by 4 · depth 21
• Commutativity of the local spherical Hecke algebra of GL₂ LocalGL2.localHeckeMul_comm 0 below · cited by 2 · depth 21
• Uniqueness of ordered Cartan representatives for 2×2 matrices LocalGL2.cartanDiag_cartanRel_iff 0 below · cited by 4 · depth 22
• Nonzero Whittaker functional for smooth GL₂ representations with nontrivial unipotent action LocalGL2.exists_whittakerFunctional_ne_zero_of_isSmoothRep_of_unipotentGL2_apply_ne 0 below · cited by 2 · depth 25
• Multiplying a Kirillov function by the indicator of a ball LocalGL2.exists_mem_forall_diagonal_mul_sub_mem_span_and_mem_span 0 below · cited by 1 · depth 27
• Non-cuspidal irreducible admissible GL₂(Kᵥ) representations admit Borel eigenfunctionals LocalGL2.exists_borelEigenfunctional_ne_zero_of_span_unipotentGL2_sub_ne_top 2 below · cited by 1 · depth 28
• Cartan decomposition of GL₂(K) over a discrete valuation ring LocalGL2.existsUnique_mem_doubleCoset_zpow 2 below · cited by 4 · depth 30
• Word coset count at central-times-unipotent elements equals walk count LocalGL2.sum_indicator_word_inv_mul_scalar_mul_unipotentGL2_mem_localIntegralSet_eq_walkCount 8 below · cited by 2 · depth 30
• Counting Hecke words of length k by tree walk numbers LocalGL2.sum_indicator_integralSubgroup_ofFn_prod_inv_mul_eq_walkCount_of_mem_doubleCoset_zpow 6 below · cited by 6 · depth 31
• Unipotent matrices in Cartan double cosets over K LocalGL2.unipotentGL2_mem_doubleCoset_diagPi_zpow_neg_mul_localRepInf_zpow 0 below · cited by 1 · depth 31
• Cartan cell of an upper-triangular element of GL₂(K) LocalGL2.mem_doubleCoset_diagPi_zpow_mul_localRepInf_zpow_iff_of_upperTriangular 1 below · cited by 4 · depth 32

LocalGL2.Kirillov 1

• Existence of bump functions in the Kirillov space LocalGL2.Kirillov.exists_isBump 1 below · cited by 1 · depth 26