https://metaphor.ethz.ch/x/2021/hs/401-3225-00L/ex/exsheet2.pdf
... (Examples of Haar Measures). a) Let us consider the three-dimensional Heisenberg group H = Roη R2, where η ... that the Lebesgue measure is the Haar measure of R oη R2 and that the group is unimodular. b) Let P ... (Examples of Haar Measures). a) Let us consider the three-dimensional Heisenberg group H = Roη R2, where η ... that the Lebesgue measure is the Haar measure of R oη R2 and that the group is unimodular. b) Let P ...
http://edu.itp.phys.ethz.ch/hs10/sqit/ex04.pdf
... scaling) unique left-invariant integration measure, the Haar measure dg:∫ G f(g)dg = ∫ G f(hg)dg for all ... functions f : G → C and all h ∈ G. The goal of this exercise is to find an expression for the Haar measure ... scaling) unique left-invariant integration measure, the Haar measure dg:∫ G f(g)dg = ∫ G f(hg)dg for all ... functions f : G → C and all h ∈ G. The goal of this exercise is to find an expression for the Haar measure ...
https://metaphor.ethz.ch/x/2020/hs/401-3225-00L/ex/ex2.pdf
... ) Show that if G is connected then X is connected. Exercise 3.(Examples of Haar Measures): a) Let us ... Lebesgue measure is the Haar measure of RoηR2 and that the group is unimodular. b) Let P = a ... ) Show that if G is connected then X is connected. Exercise 3.(Examples of Haar Measures): a) Let us ... Lebesgue measure is the Haar measure of RoηR2 and that the group is unimodular. b) Let P = a ...
https://metaphor.ethz.ch/x/2017/hs/401-3370-67L/sc/Joost1.pdf
... Haar measures Student seminar on homogeneous dynamics Joost Opschoor ojoost@student.ethz.ch Friday ... 20 October and Monday 27 October, 2017 Contents 1 Recap left-invariant Haar measures ... Haar measures Student seminar on homogeneous dynamics Joost Opschoor ojoost@student.ethz.ch Friday ... 20 October and Monday 27 October, 2017 Contents 1 Recap left-invariant Haar measures ...
https://metaphor.ethz.ch/x/2021/fs/401-3226-00L/ex/ex1.pdf
... not what one gets “group-theoretically” by using the Haar measures µG and µK with their standard ... (bi-invariant) Haar measure on µG, which is not as easy as it is for GLn(R), where we can just write ... not what one gets “group-theoretically” by using the Haar measures µG and µK with their standard ... (bi-invariant) Haar measure on µG, which is not as easy as it is for GLn(R), where we can just write ...
https://metaphor.ethz.ch/x/2018/fs/401-3370-67L/sc/PatrickTalk2.pdf
... |ΓH ∩Bt| |Z2prim ∩Bt|, |SL2(Z) · i ∩Bt| Setup and recall • Let mG be a Haar measure on a unimodular ... group G. • Let Γ < G be a lattice, on which we choose the counting measure as the Haar measure. • As ... |ΓH ∩Bt| |Z2prim ∩Bt|, |SL2(Z) · i ∩Bt| Setup and recall • Let mG be a Haar measure on a unimodular ... group G. • Let Γ < G be a lattice, on which we choose the counting measure as the Haar measure. • As ...
https://metaphor.ethz.ch/x/2020/hs/401-3225-00L/ex/sol2.pdf
... components to connected components and again that ϕ(G) = X. Exercise 3.(Examples of Haar Measures): a) Let us ... Lebesgue measure is the Haar measure of RoηR2 and that the group is unimodular. Solution: Denote by µ the ... components to connected components and again that ϕ(G) = X. Exercise 3.(Examples of Haar Measures): a) Let us ... Lebesgue measure is the Haar measure of RoηR2 and that the group is unimodular. Solution: Denote by µ the ...
https://metaphor.ethz.ch/x/2021/hs/401-3225-00L/ex/sol2.pdf
... to connected com- ponents and again that ϕ(G) = X. Exercise 2 (Examples of Haar Measures). We start ... the Lebesgue measure is the Haar measure of R oη R2 and that the group is unimodular. Solution. Denote ... to connected com- ponents and again that ϕ(G) = X. Exercise 2 (Examples of Haar Measures). We start ... the Lebesgue measure is the Haar measure of R oη R2 and that the group is unimodular. Solution. Denote ...
iac22-Rivano_Prize.pdf
... 2022 Early Career Poster Award IAC 2012 Conference Chairperson HAAR President Coordinator Athens ... 2022 Early Career Poster Award IAC 2012 Conference Chairperson HAAR President Coordinator Athens ...
https://metaphor.ethz.ch/x/2018/fs/401-3226-00L/ex/ex1.pdf
... , let us come back to the general case. First of all, we have to find a (bi-invariant) Haar measure on ... semester, we gave a Haar measure for SL2(R) by decomposing it as a measure on the upper half planeH and on ... , let us come back to the general case. First of all, we have to find a (bi-invariant) Haar measure on ... semester, we gave a Haar measure for SL2(R) by decomposing it as a measure on the upper half planeH and on ...
